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Solve for : 24 7x x
7 24x
Monday’s Warm Up
717x
7
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Objective
By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains multiple letters
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Example #1
Solve for x Solve for x
24 7x d x p 7 24x
17x
x p d
x d p
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Example #2
Solve for t Solve for t
35 5t d rt5 35t
7t
rt d
td
r
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Example #3
Solve for l Solve for l
60 5 4l V lwh5 4 60l 20 60l
lwh V
lV
wh3l
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Example #4
Solve for b Solve for b
10 3 4b z br p 10 3 4b
3 6b
z pbr pbr z
2b zbr p
r r
b
p z
r
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Example #5
Solve for t Solve for t
2 5 35t 2s t r 10 35t
25t 2s rt
2st r
25t 1 1 2t r s
2t r s
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Example #6
Solve for p Solve for p
456
p
ph
n
456
p
270p p hn
645 6
1 6
p
ph
n
1
nh n
n
p
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Example #7
Solve for r Solve for r
78.5 2 3.14 r 2C r
12.5r 2r
C
6.28 78.5
6.28 6.28
r
2 Cr 2
2 2
Cr
6.28 78.5r
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Example #8
Solve for l Solve for l
160 2 2 15l 2 2P l w
65l
2 130l
2 2l w P 2 30 160l 2 2l P w
2
2 2
w Pwl
P
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Example #9
Solve for x Solve for x
5 4 3 32x x ax b cx d
2 4 32x
x xa c b d 5 3 4 32x x a c bx d
2 28x 14x
a c dx b
a c d b
a c a c
x
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Example #9
Solve for x Solve for x
5 4 3 32x x
2 4 32x 5 3 4 32x x
2 28x 14x
a c d b
a c a c
x
xd b
a c
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Example #10
1Solve for b 1Solve for b
112120 5 3b
1 3 48b
112 5 3 120b
12 11 2 5 3 120 2b
15 3 2405 5
b
1 45b
11 22A h b b
12 1 2h Ab b
12 1
21 2 2bh b A 21 2h b Ah h
b 2
21Ahbb
21 2
Ahb b
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Motion Problem Set Ups3. Lois rode her bike to visit a friend. She traveled at 10 mi/h. While she was there, it began to rain. Her friend drove her home in a car traveling at 25 mi/h. Lois took 1.5 h longer to go to her friend’s than to return home. How many hours did it take Lois to ride to her friend’s house?
Distance
to by bike
home by
1.510 10
car 25 25
1.5t
Rate Ti
mph
mph
me
t
t t
1.510 25t t
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Motion Problem Set Ups4. Fred begins walking toward John’s house at 3 mi/h. John leaves his house at the same time and walks toward Fred’s house on the same path at a rate of 2 mi/h. How long will it be, in minutes, before they meet if the distance between the houses is 4 miles?
Distance
Fred 3 3
J 2 2ohn
t t
Rate
mph
m
ime
ph t
T
t
3 2 4t t
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Motion Problem Set Ups5. May rides her bike the same distance that Leah walks. May rides her bike 10 km/h faster than Leah walks. If it takes May 1 h and Leah 3 h to travel that distance, how fast does each travel?
Distanc
10 10
e
Ma
L h 3
y
e
1
3a
r
Rate Ti
hr r
r
m
r
e
hr
0 31r r
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Motion Problem Set Ups6. A train leaves the station at 6:00 P.M. traveling west at 80 mi/h. On a parallel track, a second train leaves the station 3 hours later traveling west at 100 mi/h. At what time will the second train catch up with the first?
Distance
First Train
Second Trai
8
3 3
0 80
100 100n
mph t t
t
Rate Time
mph t
80 10 30t t
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Motion Problem Set Ups7. At 10:00 A.M., a car leaves a house at a rate of 60 mi/h. At the same time, another car leaves the same house at a rate of 50 mi/h in the opposite direction. At what time will the cars be 330 miles apart?
60
Distance
First Car
Second
60
50Car 50
m
Rate Tim
ph
mph
e
t t
t t
60 50 330t t
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Motion Problem Set Ups
8. It takes 1 hour longer to fly to St. Paul at 200 mi/h than it does to return at 250 mi/h. How far away is St. Paul?
Distance
Fly to St. Paul
Rtn from St.
1 120
Paul
0 200
250 250
t
Rate Ti
mph
mp t
m
h t
e
t
1200 250t t
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Tuesday Night’s HomeworkSolve Each of today’s worksheet problems
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Wednesday Warm UpThe Charlestown Chiefs football team scored 10 times for a total of 46 points. If a touchdown is worth 7 points and a field goal is worth 3 points, how many touchdowns and how many field goals did the Chiefs score?
7 3 10 46x x # of Touchdowns:
# of Field Goals: 0 1
x
x 7 30 3 46x x 4 30 46x
4 16x 4x
# of Touchdowns:
# of Field Goals
4
: 6
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Two jets leave Dallas at the same time and fly in opposite
directions. One is flying west 50 mi/h faster than the other.
After 2 hours, they are 2500 miles apart. Find the speed of
each jet.
How are the distances that the two jets fly related
Distance flown by 1st Jet + Distance flown by 2nd jet = 2500 mi
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Two jets leave Dallas at the same time and fly in opposite
directions. One is flying west 50 mi/h faster than the other.
After 2 hours, they are 2500 miles apart. Find the speed of
each jet.
How are the times that the two jets fly related
The time of flight of 1st Jet = The time of flight of 2nd Jet
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Two jets leave Dallas at the same time and fly in opposite
directions. One is flying west 50 mi/h faster than the other.
After 2 hours, they are 2500 miles apart. Find the speed of
each jet.
How are the speeds of the two jets fly related
Speed of Westbound Jet = Speed of Eastbound Jet + 50 mi/hr
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Two jets leave Dallas at the same time and fly in opposite
directions. One is flying west 50 mi/h faster than the other.
After 2 hours, they are 2500 miles apart. Find the speed of
each jet. Define: Let x = the speed of the jet flying east.
Write: 2 x + 2( x + 50 ) = 2500
Then x + 50 = the speed of the jet flying west.
Relate: eastbound jet’s plus westbound jet’s equals the total distance distance distance
Jet Rate Time Distance Traveled
Eastbound x 2 2x
Westbound x + 50 2 2(x + 50)
Eastbound
Westbound
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Two jets leave Dallas at the same time and fly in opposite
directions. One is flying west 50 mi/h faster than the other.
After 2 hours, they are 2500 miles apart. Find the speed of
each jet.
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Two jets leave Dallas at the same time and fly in opposite
directions. One is flying west 50 mi/h faster than the other.
After 2 hours, they are 2500 miles apart. Find the speed of
each jet.
Jet Rate Time Distance Traveled
Eastbound x 2 2x
Westbound x + 50 2 2(x + 50)
Eastbound
Westbound
Westbound Jet: 650mph Eastbound Jet: 600mph
2 2 100 2500
4 100 2500
4 2400
600
x x
x
x
x mph
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1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?
Rate Time DistanceNorthboundSouthbound
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1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?
Rate Time DistanceNorthbound 83 mphSouthbound 67 mph
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1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?
Rate Time DistanceNorthbound 83 mph tSouthbound 67 mph t
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1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?
Rate Time DistanceNorthbound 83 mph t 83tSouthbound 67 mph t 67t
83 67 600t t
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2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?
Rate Time DistanceRomeoJuliet
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2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?
Rate Time DistanceRomeo 5 m/sJuliet 4 m/s
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2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?
Rate Time DistanceRomeo 5 m/s tJuliet 4 m/s t – 3
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2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?
Rate Time DistanceRomeo 5 m/s t 5tJuliet 4 m/s t – 3 4(t – 3)
5 4 3 87t t
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3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?
Rate Time DistanceBad Bart
Police Helo
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3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?
Rate Time DistanceBad Bart 70 mph
Police Helo 100 mph
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3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?
Rate Time DistanceBad Bart 70 mph t
Police Helo 100 mph t – .5
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3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?
Rate Time DistanceBad Bart 70 mph t 70t
Police Helo 100 mph t – .5 100(t – .5)
70 100 .5t t
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4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?
Rate Time DistanceUphill
Downhill
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4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?
Rate Time DistanceUphill 4 mph
Downhill 20 mph
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4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?
Rate Time DistanceUphill 4 mph t
Downhill 20 mph 3 - t
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4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?
Rate Time DistanceUphill 4 mph t 4t
Downhill 20 mph 3 - t 20(3 - t )
4 20 3t t
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Wednesday Night’s Homework
Complete a D = RT table for each problem. Then use the table to construct an equation.
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Thursday Warm Up
Solve each of the problems from last night’s homework.
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1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?
Rate Time DistanceCamel #1Camel #2
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1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?
Rate Time DistanceCamel #1 9 km/hrCamel #2 7 km/hr
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1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?
Rate Time DistanceCamel #1 9 km/hr tCamel #2 7 km/hr t
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1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?
Rate Time DistanceCamel #1 9 km/hr t 9tCamel #2 7 km/hr t 7t
9 7 60t t
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2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.
Rate Time DistanceCamel #1Camel #2
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2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.
Rate Time DistanceCamel #1 r km/hrCamel #2 (r + 3)km/hr
![Page 52: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/52.jpg)
2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.
Rate Time DistanceCamel #1 r km/hr 4 hrCamel #2 (r + 3)km/hr 4 hr
![Page 53: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/53.jpg)
2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.
Rate Time DistanceCamel #1 r km/hr 4 hr 4rCamel #2 (r + 3)km/hr 4 hr 4(r+3)
4 4 3 68r r
![Page 54: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/54.jpg)
3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?
Rate Time Distance1st Plane2nd Plane
![Page 55: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/55.jpg)
3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?
Rate Time Distance1st Plane 270 mph2nd Plane 450 mph
![Page 56: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/56.jpg)
3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?
Rate Time Distance1st Plane 270 mph t2nd Plane 450 mph t – 2
![Page 57: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/57.jpg)
3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?
Rate Time Distance1st Plane 270 mph t 270t2nd Plane 450 mph t – 2 450(t – 2)
270 450 2t t
![Page 58: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/58.jpg)
4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.
Rate Time DistanceEastboundWestbound
![Page 59: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/59.jpg)
4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.
Rate Time DistanceEastbound 420 mphWestbound 350 mph
![Page 60: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/60.jpg)
4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.
Rate Time DistanceEastbound 420 mph tWestbound 350 mph t – 2
![Page 61: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/61.jpg)
4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.
Rate Time DistanceEastbound 420 mph t 420tWestbound 350 mph t – 2 350(t – 2)
420 450 2 3535t t
![Page 62: Monday’s Warm Up. Objective By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains](https://reader035.vdocuments.us/reader035/viewer/2022062801/56649e6f5503460f94b6d17f/html5/thumbnails/62.jpg)
Thursday Homework
Study for uniform motion quiz by doing practice problems