Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1
Solving a Motion Problem (Motion in the Same Direction)

Jeff can bike to work in When he takes the bus, the trip takes If the bus trav-


els 20 mph faster than Jeff rides his bike, how far is it to his workplace?


Step 1 Readthe problem. We must find the distance between Jeff ’s home and his


workplace.


Step 2 Assign a variable.Although the problem asks for a distance, it is easier here


to let xbe Jeff ’s rate when he rides his bike to work. Then the rate of the bus


is


For the trip by bike,


For the trip by bus,


Summarize this information in a table.


d= rt= 1 x+ 202 #


1


4


=


1


4


1 x+ 202.


d= rt=x#


3


4


=


3


4


x.


x+ 20.


1

4 hr.


3

4 hr.


EXAMPLE 3


SECTION 2.4 Further Applications of Linear Equations 83


Rate Time Distance

Bike x

Bus
1
4 1 x+^202

1

x+ (^204)
3
4
(^3) x
4
Same


Step 3 Write an equation.The key to setting up the correct equation is to


understand that the distance in each case is the same. See FIGURE 7.


Home Workplace

FIGURE 7

The distance is the same
in each case.

Step 4 Solve. Multiply by 4.


Multiply;
Subtract x.
Divide by 2.

Step 5 State the answer.The required distance is


Step 6 Checkby finding the distance using


d=


1


4


1 x+ 202 =


1


4


110 + 202 =


30


4


=7.5 mi.


d=


3


4


x=


3


4


1102 =


30


4


= 7.5 mi.


x= 10


2 x= 20


3 x= x+ 20 1 x=x


4 a


3


4


xb = 4 a


1


4


b1x+ 202


3


4


x=


1


4


1 x+ 202


The same
result

NOW TRY

As in Example 3,the equation for a problem involving motion in the samedirec-


tion is usually of the following form.


one distanceother distance


NOW TRY
EXERCISE 3
Michael Good can drive to
work in hr. When he rides his


bicycle, it takes hours. If
his average rate while driving
to work is 30 mph faster than
his rate while bicycling to
work, determine the distance
that he lives from work.


(^1 12)
1
2
NOW TRY ANSWER



  1. 22.5 mi

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