Math Word Problems Demystified - A Self Teaching Guide

EVALUATION: Check to see if the distance the freight train travels is the
same as the AMTRAK train; that is, 105 miles.

D¼RT

D¼ 15 ð 3 þ 4 Þ

D¼105 miles

Another type of distance problem is one where two vehicles are going in
the opposite direction.

EXAMPLE:Two automobiles are leaving from the same point and are
traveling in opposite directions. One is going 10 miles per hour faster than the
other is. After traveling two hours, they are 160 miles apart. How fast is each
automobile traveling?

SOLUTION:

GOAL: You are being asked to find the speed in miles per hour that each
automobile was traveling.

STRATEGY: Draw a diagram showing that each automobile is traveling in
the opposite direction. See Figure 13-3. Letx¼the rate (speed) of the first
automobile andxþ 10 ¼the rate (speed) of the second automobile. Place
these values in the boxes under Rate. Then the time each automobile travels
is 2 hours, so place these numbers in the boxes under Time. The expressions
that represent the distances are 2xand 2(xþ10), so place these in the boxes
under Distance.

Rate  Time ¼ Distance

First automobile x 22 x

Second automobile xþ 10 2 2(xþ10)

Fig. 13-3.

LESSON 13 Solving Distance Problems 135