OBJECTIVE 2 Solve problems about uniform motion.
82 CHAPTER 2 Linear Equations, Inequalities, and Applications
Uniform motion problems use the distance formula When rate (or
speed) is given in miles per hour, time must be given in hours. Draw a sketch
to illustrate what is happening. Make a tableto summarize given information.
d=rt.
PROBLEM-SOLVING HINT
Solving a Motion Problem (Motion in Opposite Directions)Two cars leave the same place at the same time, one going east and the other west.
The eastbound car averages 40 mph, while the westbound car averages 50 mph. In
how many hours will they be 300 mi apart?
Step 1 Readthe problem. We are looking for the time it takes for the two cars to be
300 mi apart.
Step 2 Assign a variable.A sketch shows what is happening in the problem. The
cars are going in oppositedirections. See FIGURE 6.
EXAMPLE 2
50 mph 40 mphW
Total distance 300 miEStarting
pointFIGURE 6Let xrepresent the time traveled by each car, and summarize the information
of the problem in a table.
Rate Time Distance
Eastbound Car 40 x 40 x
Westbound Car 50 x 50 x
300Fill in each distance by
multiplying rate by time, using
the formula The sum of
the two distances is 300.d=rt.Step 3 Write an equation.The sum of the two distances is 300.
Step 4 Solve. Combine like terms.
Divide by 90; lowest termsStep 5 State the answer.The cars travel or 3 hr, 20 min.
Step 6 Check.The eastbound car traveled The westbound car
traveled for a total distance of
as required. NOW TRY
4003 +
5003 =
900(^50) A 3 =300 mi,
10
3 B =
5003 mi,
(^40) A^103 B =^4003 mi.
10
3 =^3
13 hr,
x=
300
90
=
10
3
90 x= 300
40 x+ 50 x= 300
CAUTION It is a common error to write 300 as the distance traveled by each car
in Example 2.Three hundred miles is the totaldistance traveled.
As in Example 2,in general, the equation for a problem involving motion in
oppositedirections is of the following form.
partial distancepartial distancetotal distance
NOW TRY
EXERCISE 2
Two trains leave a city travel-
ing in opposite directions.
One travels at a rate of 80 km
per hr and the other at a rate
of 75 km per hr. How long
will it take before they are
387.5 km apart?
NOW TRY ANSWER
- 2 12 hr