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
click here to see the step by step solution of th equation:
3v = 3*25 = 75 km/h
the rate of the motorcycle is 75 km/h.
the rate of the bicycle is 25 km/h.