Question

A car and a motorcycle whose average rates are in the ratio of 4:5 travel a distance of 160 miles. If the motorcycle travels 1/2 hour less than the car, find the average rate of each.

Answer 1

4:5
means the is 4/5 the speed of the motorcycle
d=s*t

160=s1*(t)
160=s2*(t-30)

s1*(t)=s2*(t-30)
4/5s2*t=s2*(t-30)
4/5s2*t-s2*t=-30*s2

cancel out s2
4/5*t-t=-30
-1/5t=-30
t=150

d=s1*t
160=s1*(5/2h)
s1=64

d=s2*t
160=s2(2h)
s2=80

64:80
8:10
4:5

Answer 2

In this problem you have 3 equations and 3 unknowns. The 3 unknowns are Sc, Sm, and t
(speed of the car, speed of the motorcycle, and the time traveled t in hours)

the ratio they give tells you
\[ \frac{Sc}{Sm}= \frac{4}{5} \]