The regular bus, having passed half of the route at a speed of 45 km / h, made an emergency stop for 10 minutes

The regular bus, having passed half of the route at a speed of 45 km / h, made an emergency stop for 10 minutes. To make up for the lost time, the bus increased the speed by 15 km / h. Find the length of the route.

Let’s say that the length of the route is x km.

At a speed of 45 km / h, the bus will travel this distance in x / 45 hours.

The bus traveled half the way at a speed of 45 km / h, which means it took x / 90 hours.

When the bus increased its speed by 15 km / h, its speed was 60 km / h and it covered half the way in x / 120 hours.

Let’s compose and solve the equation:

x / 45 – 1/6 = x / 90 + x / 120,

(2 * x – 15) / 90 = (4 * x + 3 * x) / 360,

(2 * x – 15) / 90 = 7 * x / 360,

72 * x – 540 = 63 * x,

9 * x = 540,

x = 540: 9,

x = 60 (km).