A car can travel 100 miles in the same time that it takes a bus to travel 80 miles. If the rate of the bus is 10 miles per hour slower than the car, find the average rate for each

the rate of the car is 50 mph.

Step-by-step explanation:

Let x represent the rate of the car. If the rate of the bus is 10 miles per hour slower than the car, it means that the rate of the bus is (x - 10) mph.

Time = distance/speed

The car can travel 100 miles in the same time that it takes a bus to travel 80 miles. It means that the time taken by the bus to travel 100 miles is

100/x

and the time taken by the car to travel 80 miles is

80/(x - 10)

Since the time is the same, then

80/(x - 10) = 100/x

Cross multiplying, it becomes

80x = 100(x - 10)

80x = 100x - 1000

100x - 80x = 1000

20x = 1000

x = 1000/20

x = 50 mph