math word problem

Question

a car travel 300 miles in the same amount of time it takes a bus to travel 180 miles. If the rate of the bus is 20 miles per hour slower than the rate of the car, find the average rate for each.

Answer 1

Car  300 miles  =  r  mi/hr  ( time)

       300 =  r   t

Bus  180 miles =  (r-20) mi/hr   ( time )

       180  = (r-20)  t

The times are the same

180 / (r-20)    =   300 /r

Cross multiply and solve to get 

r = 50 mi/hr  for the car

r-20 = 30 mi/hr  for the bus

 

Car Time = t  =  300/50 = 6 hours

Bus Time = t  =  180 / (50-20) = 6 hours