Math Word Problems Demystified - A Self Teaching Guide

If you look at Figure 13-3, you will see that the total distance is thesum

of the individual distances each car went, since each is going in the opposite

direction: 2xþ2(xþ10)¼160.

IMPLEMENTATION: Solve the equation forx:

2 xþ 2 ðxþ 10 Þ¼ 160

2 xþ 2 xþ 20 ¼ 160

4 xþ 20 ¼ 160

4 xþ 20 
 20 ¼ 160 
 20

4 x¼ 140

41 x

41

¼

140

4

x¼35 miles per hour

xþ 10 ¼ 35 þ 10 ¼45 miles per hour

Hence the slower automobile was traveling at 35 miles per hour and the

faster automobile was traveling at 45 miles per hour.

EVALUATION: We can find the distance each automobile traveled and then

see if the sum is 160 miles.

Automobile 1: D¼RT

D¼ 35  2 ¼70 miles

Automobile 2: D¼RT

D¼ 45  2 ¼90 miles

Hence, 70þ 90 ¼160 miles.

Try These

1. Two people leave from two towns that are 195 miles apart at the same
   time and travel along the same road toward each other. The first

136 LESSON 13 Solving Distance Problems