Math Word Problems Demystified - A Self Teaching Guide

lett¼the time the AMTRAK train travels and placetin the top box under

Time. Let (tþ4) be the time the freight train travels and place (tþ4) in the

lower box under time. The freight train travels 4 more hours since it left

earlier. To get the distance for each train, multiply the rate by the time and

place these expressions under Distance.

Rate  Time ¼ Distance

AMTRAK 35 t 35 t

Freight train 15 tþ 4 15(tþ4)

Since the distances each train travels are the same, the equation is

35 t¼15(tþ4).

IMPLEMENTATION: Solve the equation:

35 t¼ 15 ðtþ 4 Þ

35 t¼ 15 tþ 15  4

35 t¼ 15 tþ 60

35 t
 15 t¼ 15 t
 15 tþ 60

20 t¼ 60

201 t

201

¼

60

20

t¼3 hours

To find the distance, use the formulaD¼RT.

D¼RT

D¼ 35  3

¼105 miles

Hence the AMTRAK train will overtake the freight train 105 miles

from Pittsburgh.

134 LESSON 13 Solving Distance Problems