story problems ii
DESCRIPTION
STORY PROBLEMS II. THE “REALLY TOUGH STUFF”. General Directions for d = rt problems. Read the problem carefully. Ask yourself, “What am I trying to find.” Determine what kind of a problem it is. Write your equation and solve Ask yourself, “Did I answer the question asked?”. - PowerPoint PPT PresentationTRANSCRIPT
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STORY PROBLEMS II
THE “REALLY TOUGH STUFF”
![Page 2: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/2.jpg)
General Directions for d = rt problems
1. Read the problem carefully.2. Ask yourself, “What am I trying to
find.”3. Determine what kind of a problem
it is.4. Write your equation and solve5. Ask yourself, “Did I answer the
question asked?”
![Page 3: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/3.jpg)
A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? What am I trying to find?How long does it take the MOTORBOAT to catch the canoe. In other words, how long is the motorboat on the water?
![Page 4: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/4.jpg)
A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? This problem contains speed (rate) and
time.
![Page 5: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/5.jpg)
A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? Use d = rt Make a table of the information.
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoeMotorboat
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoe 12Motorboat
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoe 12Motorboat 21
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoe 12 tMotorboat 21
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoe 12 tMotorboat 21 t - 2
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoe 12 t 12tMotorboat 21 t - 2
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
Rate Time DistanceCanoe 12 t 12tMotorboat 21 t - 2 21(t - 2)
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe? The motorboat has caught the canoe
(same direction) The distances traveled by both must be
the same. Set the two distances equal to each
other and solve.
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
12 𝑡=21(𝑡−2)
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
12 𝑡=21(𝑡−2)
12 𝑡=21𝑡−42
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
12 𝑡=21(𝑡−2)
12 𝑡=21𝑡−42−9𝑡=−42
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
12 𝑡=21(𝑡−2)
12 𝑡=21𝑡−42−9𝑡=−42
𝑡=−42−9
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
)
12 𝑡=21𝑡−42−9𝑡=−42
𝑡=−42−9 =4.6
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
)
12 𝑡=21𝑡−42−9𝑡=−42
𝑡=−42−9 =4.6
You can convert your answer to hours and minutes if you like.
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A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
12 𝑡=21¿
12 𝑡=21𝑡−42−9𝑡=−42
𝑡=−42−9 =4.6
You can convert your answer to hours and minutes if you like.The time you have found is the time for the canoe. You were not asked to find that. Find the motorboat’s time.
![Page 21: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/21.jpg)
A canoe leaves a campsite and travels at an average speed of 12 mph. Two hours later, a motorboat leaves the campsite and travels an average rate of 21 mph. After how many hours does the motorboat catch the canoe?
12 𝑡=21¿
12 𝑡=21𝑡−42−9𝑡=−42
𝑡=−42−9 =4 .6It takes the motorboat 2 hours and 40 minutes to catch the canoe. Or you can just leave it hours.
You can convert your answer to hours and minutes if you like.The time you have found is the time for the canoe. You were not asked to find that. Find the motorboat’s time.
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Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4 km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you arrive at the top of the hill? This problem contains rate and time
(but it is given as “clock” time.) If you go to a location, then come
back, you have a “round trip” situation
In a round trip, the distances are equal.
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Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? Make a table. Add a column for the “clock” time.
![Page 24: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/24.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
UpDown
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Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4Down
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Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4Down 6
![Page 27: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/27.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4 tDown 6
![Page 28: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/28.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4 tDown 6 3 - t
![Page 29: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/29.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4 t 4tDown 6 3 - t
![Page 30: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/30.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4 t 4tDown 6 3 - t 6(3 – t)
![Page 31: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/31.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4 t 4t 9:00 amDown 6 3 - t 6(3 – t)
![Page 32: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/32.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill?
Rate Time Distance
Clock
Up 4 t 4t 9:00 amDown 6 3 - t 6(3 – t) ????
![Page 33: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/33.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)
![Page 34: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/34.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡
![Page 35: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/35.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18
![Page 36: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/36.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18
𝑡=1810
![Page 37: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/37.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18
𝑡= 1810=1.8hours
![Page 38: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/38.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18
𝑡= 1810=1.8hours
This does NOT answer the question asked. This is how long it takes to get to the top of the hill, not AT WHAT TIME?
![Page 39: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/39.jpg)
Suppose you begin to hike up a hill at 9:00 a.m. at an average rate of 4
km/hr. You hike back down the hill at an average rate of 6 km/hr. If you arrive back at your campsite at 12:00 p.m., at what time did you
arrive at the top of the hill? 4 𝑡=6 (3−𝑡)4 𝑡=18−6 𝑡10 𝑡=18
𝑡=1810=1.4 hours
This does NOT answer the question asked. This is how long it takes to get to the top of the hill, not AT WHAT TIME?
If you left at 9:00 am, and it took 1.8 hours (or 1 hour 48 minutes), then you arrived at the top of the hill at 10:48 am.
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Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the jets are 1250 miles apart. Find the speed of each jet.
The jets are flying in “opposite directions.”
To solve an opposite direction problem, ADD the distances traveled to find the distance apart.
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Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Make a table.
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Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestboundEastbound
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Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25Eastbound
![Page 44: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/44.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25Eastbound r
![Page 45: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/45.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2Eastbound r
![Page 46: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/46.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2Eastbound r 2
![Page 47: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/47.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2
![Page 48: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/48.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r
![Page 49: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/49.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r
2𝑟+2 (𝑟+25 )=1250
![Page 50: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/50.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r
2𝑟+2 (𝑟+25 )=1250
2𝑟+2𝑟+50=1250
![Page 51: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/51.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r
2𝑟+2 (𝑟+25 )=1250
2𝑟+2𝑟+50=12504𝑟+50=1250
![Page 52: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/52.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r+25)Eastbound r 2 2r
2𝑟+2 (𝑟+25 )=1250
2𝑟+2𝑟+50=12504𝑟+50=1250
4𝑟=1200
![Page 53: STORY PROBLEMS II](https://reader036.vdocuments.us/reader036/viewer/2022062501/56816689550346895dda42a4/html5/thumbnails/53.jpg)
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r + 25)Eastbound r 2 2r
2𝑟+2 (𝑟+25 )=1250
2𝑟+2𝑟+50=12504𝑟+50=1250
4𝑟=1200𝑟=300
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Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 25 mi/hr faster than the other. After 2 hours, the
jets are 1250 miles apart. Find the speed of each jet.
Rate Time DistanceWestbound r + 25 2 2(r +25)Eastbound r 2 2r
2𝑟+2 (𝑟+25 )=1250
2𝑟+2𝑟+50=12504𝑟+50=1250
4𝑟=1200𝑟=300
The rate (r) is the rate of the eastbound jet. Therefore, the westbound jet is flying at 325 mph.
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Wrap-up There are three type of problems. Same direction Round-trip Opposite direction In same direction and round-trip
problems, you set the distances equal to each other.
In opposite direction, you add the distances together.
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Assignment2.5B: 10 - 24