A bus and a cyclist leave a school at 8 am and head for a st

A bus and a cyclist leave a school at 8 am and head for a stadium 90mi away. The rate of the bus is three times the rate of the cyclist. The cyclist arrives 4h after the bus. Find the rate of the bus

Solution

rate of the bus = B
rate of the cyclist = C
distance traveled = 90 miles
time taken by the bus = 90/B
time taken by the cyclist = 90/C

B = 3C
90/C = 4 + 90/B
90/C = 4 + 90/(3C)
90/C = 4 + 30/C
90/C - 30/C =4
60/C = 4
C = 60/4 = 15
B = 3C = 3*15 = 45

so,the rate of the bus is 45 miles/hour