ms algebra ch. 7.6 uniform motion...
TRANSCRIPT
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MS Algebra – Ch. 7.6Uniform Motion Problems
Mr. Deyo
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By the end of the period, I will apply the concept of uniform motion to solve for the desired variable in a word problem.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Learning Target
Title: Uniform Motion Date:
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Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 7.6 Pg. 415-417 3) Section ______
TxtBk. Prob.#13,17,21,22,25 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
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Storm Check (Think, Write, Discuss, Report)
Questions on which to ponder and answer:1. How are the two images similar?
2. How are they different?
3. How can these two images be related to math?
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Two trains left a station in opposite directions. One traveled 50 miles per hour and the other traveled 45 miles per hour. How far apart were they after 2 hours?
For use with pages xxx–xxxDaily Warm-Up Exercises
TrainStation
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Two trains left a station in opposite directions. One traveled 50 miles per hour and the other traveled 45 miles per hour. How far apart were they after 2 hours?
For use with pages xxx–xxxDaily Warm-Up Exercises
190 milesANSWER
TrainStation
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1) System of Linear Equations
2) Distance
3) Rate (Speed)
4) Time
Vocabulary
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DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
Friendly DefinitionSketch
Wordwork Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing
DAY 1
1. Use Visuals
2. Introduce the word
Friendly Definition
Physical Representation
3. Use Cognates
4. Write friendly definition
5. Physical Representation
Word List1.2.3.4.
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Problem A
A kayaker travels upstream at a speed of 2 miles per hour
and downstream at a speed of 5 miles per hour. The speed of the current remains constant throughout the trip. Find the speed of the kayak in still water and the speed of the current.
KAYAKING
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Problem A
A kayaker travels upstream at a speed of 2 miles per hour
and downstream at a speed of 5 miles per hour. The speed of the current remains constant throughout the trip. Find the speed of the kayak in still water and the speed of the current.
Kayak 3.5 mi/h, Current 1.5 mi/h
KAYAKING SOLUTION
x – y = 2x + y = 5
2x = 7x = 3.5
ANSWERx = speed of kayaky = speed of current
3.5 + y = 5y = 1.5
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Problem B
During a kayaking trip, a kayaker travels upstream
(against the current) and downstream (with the current)
at the speeds shown below. The speed of the current
remains constant. Find the speed of the kayak in still
water and the speed of the current.
Write and solve a linear system
(ANNOTATE) KAYAKING
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Problem B
During a kayaking trip, a kayaker travels upstream (against the current) and
downstream (with the current) at the speeds shown below. The speed of the
current remains constant. Find the speed of the kayak in still water and the
speed of the current.
Write and solve a linear systemKAYAKING
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Write and solve a linear systemProblem B
STEP 1 Write a system of equations. Let
x be the speed of the kayak in
still water, and let y be the speed
of the current.
Equation 1: Going upstream
x - y = 4
Equation 2: Going downstream
x + y = 6
STEP 2 Solve the system of equations.
4yx =–
= 6yx +
102x =
5x =
Substitute 5 for x in Equation 2 and
solve for y.
6y5 =+
1y =
Write Equation 1.
Write Equation 2.
Add equations.
Solve for x.
Substitute 5 for x in
Equation 2.
Subtract 5 from each side.
1y =5x=ANSWER
SOLUTION
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Storm Check (Think, Write, Discuss, Report)
When reading the problem, what is the first and probably most difficult step in solving a linear system of equations?
The first and most difficult step in solving a system
of linear equations is ________________________
_________________________________________
_________________________________________.
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Notes:
D=RT DistanceRate
or Speed Time
1st Equation(East, 1st Boat, etc.)
2nd
Equation(West, 2nd Boat, etc.)
Total
Distance = (Rate)(Time)
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Problem A
A helicopter leaves an airport and flies north at 180 miles per hour. An hour later, an airplane leaves the airport flying in the same direction at
330 miles per hour. Write a system of equations that can be used to determine how long it will take the airplane to overtake the helicopter.
AIRCRAFTWrite a system of equations
D=RT DistanceRate
or Speed Time
Helicopter
Airplane
Total
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Problem A
A helicopter leaves an airport and flies north at 180 miles per hour. An hour later, an airplane leaves the airport flying in the same direction at
330 miles per hour. Write a system of equations that can be used to determine how long it will take the airplane to overtake the helicopter.
AIRCRAFTWrite a system of equations
D=RT DistanceRate
or Speed Time
Helicopter D 180 x
Airplane D 330 y = x - 1
Total 180x = 330y 180x =330y
y = x - 1180x = 330y180x = 330(x-1)180x = 330x-330-150x =-330
x = 2.2 hy = 2.2 – 1 = 1.2h
SOLUTION
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Write a system of equationsProblem A
STEP 2 Write a linear system. Let x be the helicopter’s
flying time, and let y be the airplane’s flying
time.
1xy –=
180y330 =• x•
AIRCRAFT
SOLUTION
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Problem B
Suppose the airplane leaves a half hour after the
helicopter. What would change in the system of
equations used to determine how long it will take the
airplane to overtake the helicopter.
WHAT IF?
y = x - 1
330y = 180x
Original Equations
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Problem B
Suppose the airplane leaves a half hour after the
helicopter. What would change in the system of
equations used to determine how long it will take the
airplane to overtake the helicopter.
y = x - 0.5330y = 180x
WHAT IF?
ANSWER
y = x - 1
330y = 180x
Original Equations
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1.2 hours
2 hours
3.2 hours
16 hours
Guided PracticeTwo people are riding on a bicycle trail. The first person begins riding 1.2 hours before the second person. The first person is riding at 5 miles per hour. The second person is
riding at 8 miles per hour. How long will it take for the second person to overtake the first person?
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1.2 hours
2 hours
3.2 hours
16 hours
ANSWER
Guided PracticeTwo people are riding on a bicycle trail. The first person begins riding 1.2 hours before the second person. The first person is riding at 5 miles per hour. The second person is
riding at 8 miles per hour. How long will it take for the second person to overtake the first person?
B
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Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 7.6 Pg. 415-417 3) Section ______
TxtBk. Prob.#13,17,21,22,25 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
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By the end of the period, I will apply the concept of uniform motion to solve for the desired variable in a word problem.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Learning Target
Title: Uniform Motion Date:
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A car was driven 312 miles at an average rate of 48miles per hour. How long did the trip take?
For use with pages xxx–xxxTicket Out
+ 10=4y3x+ 4=3y4x
Solve the linear system.
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A car was driven 312 miles at an average rate of 48miles per hour. How long did the trip take?
For use with pages xxx–xxxTicket Out
+ 10=4y3x+ 4=3y4x
ANSWER
Solve the linear system.
ANSWER
6.5 hours(-2, 4)