From one city to another, the distance between which is 240 km, a bus and a car left at the same time.

From one city to another, the distance between which is 240 km, a bus and a car left at the same time. The bus was moving at a speed 20 km / h slower than the speed of the car, and arrived at its destination 1 hour later than the car. find car speed and bus speed.

We will solve this problem using the equation.

1. Let’s denote by x the speed of the car.

2. Find the speed of the bus.

x – 20 km / h.

3. Determine how many hours the car was on the road.

240 km: x km / h = 240 / h.

4. Find how long the bus was on the way.

240 km: (x – 20) km / h = 240 / (x – 20) km.

5. Let’s compose and solve the equation.
240 / (x – 20) – 240 / x = 1;

x2 – 20x – 240x + 240x – 4800 = 0;

x2 – 20x – 4800 = 0;

D = 400 + 19200 = 19600;

The equation has 2 roots x = 80 and x = -60.

Vehicle speed cannot be less than 0, 1 root x = 80 is suitable.

6. Vehicle speed is x = 80 km / h.

7. Find the speed of the bus.

80 km / h – 20 km / h = 60 km / h.

Answer: The speed of the car is 80 km / h, and the speed of the bus is 60 km / h.