motion module

7/27/2019 Motion Module

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Word Problems - Motion

By

Joe JoynerMath 04

IntermediateAlgebra

Link to Practice Problems
http://www.tcc.edu/vml/Math04/Motion%20Module/Practice.htmhttp://www.tcc.edu/vml/Math04/Motion%20Module/Practice.htm


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In this module, youll continue to develop and work

with mathematical models.

Introduction

When solving practical application problems,

you try to find a mathematical model for the

problem.

A mathematical model does not necessarily have to

be complicated. It can be relatively simple. This isusually the case when only one or two variables are

required to build a linear model. Lets begin.


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If an object such as an automobile or an

airplane travels at a constant, or uniform,

rate of speed, r ,

then the distance traveled by the object,

d, during a period of time, t

Rate, Time, and Distance Problems


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is given by the distance, rate, time

formula: d = rt.


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Example 1

You ride your bike for 7 hours. If you travel36.75 miles, what is your average speed?


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Example 1

The quantities in this problem are:

distance(constant at 36.75 miles),

time (constant at 7 hours),

and rate, or speed (unknown

variable).


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Example 1

You can use a spreadsheet (Excel, forexample) to build a model for this problem.


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Example 1

To access the

spreadsheet,

click the word

Explore.

Then explore with the rate to see if you can

solve the problem.

d = rt

Rate (mph) Time (h) Distance (m)

Biker 7 0

Rate * Time = Distance

Biker Problem

Explore
http://localhost/var/www/apps/conversion/tmp/scratch_5/Biker.xlshttp://localhost/var/www/apps/conversion/tmp/scratch_5/Biker.xls


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Example 1

Represent the variable rate with r .

You can use the distance,rate,

time formula. d = rt


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Example 1

But since you know the distance and time, and

wish to solve forrate, it would be helpful tosolve the equation for r first.

r dt


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Example 1

is ourmathematical model.rd

t

Some mathematical models can be easy!


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Example 1

rd

t

3675

7

.

Now we can solve for the rate, r , by dividingthe distance by the time.

5.25 miles per hour


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When you read a word problem that

involves rate, time, and distance, note

whether the problem situation involves

motion in the same direction;

motion in opposite directions;

a round trip.


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Example 2

Dan and Emily are truck drivers. Dan, averaging

55 miles per hour (mph), begins a 280-mile tripfrom their companys Norfolk warehouse to

Charlotte, NC at 7 AM.

Emily sets out from the Charlotte warehouse at8 AM on the same day as Dan and travels at

45 mph in the opposite direction as the route taken

by Dan.


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Example 2

How many hours will Emily have been driving

when she and Dan pass each other?

How will you start to set up a model for solving

this problem?


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Example 2

What is the variable that you must solve for?

time

Is the length of time traveled the same for

Dan and Emily when they pass each other?

No.


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Example 2

Why is the time different for the two drivers?

Dan started at 7 AM and

Emily started at 8 AM.

Dan averaged 55 mph and

Emily averaged 45 mph.


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Example 2

Let t represent the amount oftime that Emily

travels until the trucks pass each other.

In terms of t , how long will Dan have beenon the road when the trucks pass each other?

t + 1One hour longer or ...


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Example 2

You can use a spreadsheet to build a model forthis problem too.


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Example 2

To access the

spreadsheet,

click the word

Explore.

d = rt

Rate (mph) Time (h) Distance (m)

Dan 55 1 55

Emily 45 0 0

55

Rate * Time = Distance

Total Distance

Truck Driver Problem

Then explore with Emilys time to see if you

can solve the problem.

Explore
http://localhost/var/www/apps/conversion/tmp/scratch_5/Trucks.xlshttp://localhost/var/www/apps/conversion/tmp/scratch_5/Trucks.xls


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Example 2

The mathematical model for this problem is:

Dans Distance + Emilys Distance = 280 miles

Dans rate*Dans time + Emilys rate*Emilys time = 280

55(t+1) + 45t = 280


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Example 2

55(t+1) + 45t = 280

55t+55 + 45t = 280

100t + 55 = 280

100t = 225

t = 2.25 hours


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Example 3

Jason and LeRoy are entered in a 26-mile marathon

race. Jasons average pace is 6 miles per hour(mph) and LeRoys average pace is 8 mph. Both

runners start at the same time.

How far from the finish line will Jason be when

LeRoy crosses the finish line?


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Example 3

What are the known constants?Jasons rate of 6 mph

LeRoys rate of 8 mph

Race distance of 26 miles


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Example 3

What are the unknowns? The amount oftime it takes LeRoy to

finish the race

The distance Jason has to run when

LeRoy finishes


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Example 3

Let LeRoys time be t .

What is the distance, rate, time,

model for Leroy in this problem?

8t = 26

What is the solution for t ? t = 3.25 hours


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Example 3

At the time that LeRoy crosses the finish

line, Jason has run for the same amount oftime, t .

What is the model for

how far Jason is from thefinish line at that time?

d = 26 - 6(3.25)

d = 6.5 miles


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Do you think youve got the concept of

solving motion (rate, time distance)

problems?

Look at the next slide.

If you want to try the interactive web sitethat the slide came from, click on the word

Explore to go there.


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Explore
http://math.uww.edu/~mcfarlat/141/story9j.htmhttp://math.uww.edu/~mcfarlat/141/story9j.htm


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Hopefully, you are now ready to practice motion

problems for yourself. When you click the Go To

Practice Problemslink below, your web browserwill open the practice problem set.

Go To Practice Problems
http://www.tcc.edu/vml/Math04/Motion%20Module/Practice.htmhttp://www.tcc.edu/vml/Math04/Motion%20Module/Practice.htm

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