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tristan6766
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.
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
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 \[ \frac{Sc}{Sm}= \frac{4}{5} \]