Answer: the rate of the car is 50mph
Explanation:
Let x represent the average speed of the bus.
Let y represent the distance travelled by the bus.
The average speed of the car is 30 mph slower than twice the speed of the bus. This means that the average speed of the car would be
2x - 30
Distance = speed × time
Time = distance/speed
Therefore, In 2 hours time,
2 = y/x
2x = y
In two hours the car is 20 miles ahead of the bus. Therefore
2 = (y + 20)/(2x - 30)
2(2x - 30) = y + 20
4x - 60 = y + 20 - - - - - - - - -1
Substituting y = 2x into equation 1, it becomes
4x - 60 = 2x + 20
4x - 2x = 20 + 60
2x = 80
x = 80/2 = 40
The speed of the car would be
2x - 30 = 2 × 40 - 30
= 80 - 30 = 50 mph