Math Word Problems Demystified - A Self Teaching Guide

EXAMPLE:An airplane flies from Pittsburgh to Harrisburg in 1.5 hours and

returns in 2 hours. If the wind speed is 16 miles per hour blowing from the

west, find the airspeed of the plane.

SOLUTION:

GOAL: You are being asked to find the airspeed of the plane.

STRATEGY: Letx¼the airspeed of the plane. Since Harrisburg is east of

Pittsburgh and the wind is blowing from west to east, the ground speed

from Pittsburgh to Harrisburg isxþ16. The ground speed from Harrisburg

to Pittsburgh isx
16. The times are given.

Rate  Time ¼ Distance

To Harrisburg xþ 16 1.5 1.5(xþ16)

To Pittsburgh x
 16 2 2(x
16)

Since the distances are the same, the equation is 1.5(xþ16)¼2(x
16).

IMPLEMENTATION: Solve the equation:

1 : 5 ðxþ 16 Þ¼ 2 ðx
 16 Þ

1 : 5 xþ 24 ¼ 2 x
 32

1 : 5 x
 2 xþ 24 ¼ 2 x
 2 x
 32


 0 : 5 xþ 24 
 24 ¼
 32 
 24


 0 : 5 x¼
 56


 0 : 51 x


 0 : 51

¼

56

0 : 5

x¼112 miles per hour

EVALUATION: Check to see if the distances are the same. UseD¼RT.

To Harrisburg: D¼ 1 : 5 ðxþ 16 Þ

¼ 1 : 5 ð 112 þ 16 Þ

¼ 1 : 5 ð 128 Þ

¼192 miles

142 LESSON 13 Solving Distance Problems