Answer: the rate of the car is 50 mph.
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