A passenger train departed from point M to point N at a speed of 68 km / h, and 6 minutes later an electric train

A passenger train departed from point M to point N at a speed of 68 km / h, and 6 minutes later an electric train followed it, passing 85 km per hour. At what distance from point N will the electric train catch up with the passenger if the length of the section MN is 40 km? Solve the problem by making an equation.

Let the passenger train and the electric train travel a distance equal to x km until the moment when the electric train catches up with the passenger. A passenger train will cover this distance in x / 68 hours, and an electric train in 85 / x hours. By the condition of the problem, it is known that the passenger train was on the way longer by (x / 68 – x / 85) hours, or by 6 minutes = 0.1 hours. Let’s make an equation and solve it.

x / 68 – x / 85 = 0.1;

(85x – 68x) / 5780 = 0.1;

17x = 5780 * 0.1;

17x = 578;

x = 578: 17;

x = 34 (km) trains passed from point M;

40 – 34 = 6 (km) – from point N.

Answer. 6 km.