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:48 km/hStep-by-step explanation:Given in the question,time taken by motorcyclist of he travel at constant speed = 5 hourstime taken by motorcyclist in the return trip = (5x60) - 15                                                                         = 285 minutes                                                                         = 4.75 hoursSuppose original speed = x km/h                 increased speed = (3+x) km/hFirst equationdistance = time x speed    y           = 5(x)Second equationtime = distance / speed4.75 = 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 - 36xrearrange the terms4.75x² -5x² + 14.25x = 108-0.25x² + 14.25x - 108 = 0by using quadratic equationx = 48x = 9original speed of motorcyclist is x km/h that is 48 km/h