Math Word Problems Demystified - A Self Teaching Guide

4. Lett¼the time it takes to ride to the friend’s house and 1.5
   t¼the
   time it takes to walk back.
   Rate  Time ¼ Distance

To friend’s house 9 t 9 t

Return home 3 (1.5
t) 3(1.5
t)

The distances are equal since she is making a round trip.

9 t¼ 3 ð 1 : 5 
tÞ

9 t¼ 4 : 5 
 3 t

9 tþ 3 t¼ 4 : 5 
 3 tþ 3 t

12 t¼ 4 : 5

121 t

121

¼

4 : 5

12

t¼ 0 :375 hour

D¼RT

D¼ 9  0 : 375 ¼ 3 :375 miles

5. Lett¼the time the person on the motorcycle takes to overtake the
   person on the bicycle andtþ 1 ¼the time the person on the bicycle
   rides.
   Rate  Time ¼ Distance
   Bicycle 10 tþ 1 10(tþ1)

Motorcycle 30 t 30 t

The distances are equal.

30 t¼ 10 ðtþ 1 Þ

30 t¼ 10 tþ 10

30 t
 10 t¼ 10 t
 10 tþ 10

20 t¼ 10

201 t

201

¼

10

20

t¼ 0 :5 hour

LESSON 13 Solving Distance Problems 139