Amotorcyclist 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?

48 km/h

Step-by-step 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

distance = time x speed

   y           = 5(x)

time = distance / speed

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

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