Question

A motorcyclist travelling at a constant speed covered the distance between point M and point N in 5 hours. On the return trip, the first 36 km were traveled at that same speed. For the rest of the trip, the motorcyclist increased the speed by 3 km/hour. What was the motorcyclist’s original speed if the return trip took him 15 minutes less than the trip from M to N?

Answer 1

48 and 9

Explanation:

Answer 2

48 km/h

Explanation:

Given in the question,

time taken by motorcyclist of he travel at constant speed = 5 hours

time taken by motorcyclist in the return trip = (5x60) - 15

= 285 minutes

= 4.75 hours

Suppose original speed = x km/h

increased speed = (3+x) km/h

First equation

distance = time x speed

y = 5(x)

Second equation

time = distance / speed

4.75 = 36/x + (y-36)/(x+3)

Substitute value of y in equation 2

4.75 = 36/x + (5x-36) / (x+3)

4.75x(x+3) = 36(x+3) + (5x-36)x

4.75x² + 14.25x = 36x + 108 + 5x² - 36x

rearrange the terms

4.75x² -5x² + 14.25x = 108

-0.25x² + 14.25x - 108 = 0

by using quadratic equation

x = 48

x = 9

original speed of motorcyclist is x km/h that is 48 km/h