A bus travels 180 miles in same time a car travels 240 miles. if cars speed is 15mph faster than speed of bus, find the speed of car and bus.

If the bus's speed is x, then since time = distance/speed,

180/x = 240/(x+15)

To find the speeds of the car and the bus, we can set up a system of equations based on the given information.

Let's assume the speed of the bus is 'x' mph.

According to the given information, the speed of the car is 15 mph faster than the speed of the bus, which means the speed of the car is 'x + 15' mph.

We know that time is equal to distance divided by speed.

The time it takes for the bus to travel 180 miles is:

Time_bus = Distance_bus / Speed_bus
Time_bus = 180 / x

The time it takes for the car to travel 240 miles is:

Time_car = Distance_car / Speed_car
Time_car = 240 / (x + 15)

Since the time for both the bus and the car is the same, we can equate the two equations:

180 / x = 240 / (x + 15)

We can cross-multiply to solve for x:

180(x + 15) = 240x

180x + 2700 = 240x

2700 = 240x - 180x

2700 = 60x

Dividing both sides by 60:

x = 2700 / 60

x = 45

So the speed of the bus is 45 mph.

To find the speed of the car, we substitute the value of x back into one of the equations:

Speed_car = Speed_bus + 15
Speed_car = 45 + 15
Speed_car = 60

Therefore, the speed of the car is 60 mph and the speed of the bus is 45 mph.