Naoki bikes the 36 ml to Hillsboro averaging a certain speed

Naoki bikes the 36 ml to Hillsboro averaging a certain speed, The return trip is made at speed 3 mph slower. Total time for the round trip is 7 hr. Find Naoki\'s average speed on each part of the trip.

Solution

To Hilsboro the distance = 36 mi, let x be the speed then time = 36/x

Now for return trip distance = 36 mi, now speed is x-3 hence time = 36/(x-3)

Total time = 7 hrs

=> 36/x + 36/(x-3) = 7

=> 36(x-3) + 36x = 7(x)(x-3)

=> 36x-108+36x= 7x²-21x

=> 7x² -93x + 108 = 0

(7x-9)(x-12) = 0

=> x=9/7 and 12

x=9/7 cannot be the solution and so x=12

The Naokis speed to Hilsboro = 12mi/hr

To the return trip , speed = 12-3 = 8 mi/hr