Problema Solution

A motorcycle travels three times as fast as a bicycle. The former requires 2 hours longer to cover 450 km than the latter requires to cover 100km. What is the rate if each vehicle?

Answer provided by our tutors

let


v = the rate of the bicycle, v>=0


3v = the rate of the motorcycle


d1 = 450 km the distance the motorcycle travels


t1 = the time of the motorcycle's trip


d2 = 100 km the distance the bicycle travels


t2 = the time of the bicycle's trip


The former requires 2 hours longer to cover 450 km than the latter requires to cover 100 km:


t1 = t2 + 2


since rate = distance/time we have time = distance/rate


t1 = d1/3v


t1 = 450/3v


t2 = d2/v


t2 = 100/v


plug t1 = 450/3v and t2 = 100/v into t1 = t2 + 2:


450/(3v) = (100/v) + 2


by solving we find:


v = 25 km/h


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3v = 3*25 = 75 km/h


the rate of the motorcycle is 75 km/h.


the rate of the bicycle is 25 km/h.