how long will it take a bus travelling at 60 miles per hour to overtake a car travelling at 40 mph if the car had a 1.5 hour head start

Let x = the time to overtake

60x = 1.5 + 40x

Solve for x.

Let the time taken by the bus for the trip be t hours

Let the time taken by the car for the trip be t+1.5

distance covered by bus = 60t
distance covered by car = 40(t+1.5)

60t = 40(t+1.5)
60t = 40t + 60
20t = 60
t = 3

bus goes for 3 hours and the car for 4.5 hours

check:
3x60 = 180
4.5x40 = 180

To answer this question, we need to consider the relative distance covered by the car and the bus during the head start of 1.5 hours.

Since the car is traveling at a constant speed of 40 mph, it covers a distance of 40 miles per hour x 1.5 hours = 60 miles.

The bus is traveling at a speed of 60 mph and needs to cover this 60-mile distance in order to catch up to the car.

To calculate the time required for the bus to cover this distance, we can use the formula: time = distance / speed.

So the time required for the bus to catch up to the car is: time = 60 miles / 60 mph = 1 hour.

Therefore, it will take the bus 1 hour to overtake the car.