Two trains leave at the same time from points M and N, the distance between which is 45 km, and meet in 20 minutes.

Two trains leave at the same time from points M and N, the distance between which is 45 km, and meet in 20 minutes. The train leaving M arrives at station N 9 minutes earlier than the other train at M. What is the speed of each train?

Suppose the speed of the first train is x km / h, and the speed of the second train is y km / h.

Since the trains met in 20 minutes, we can make the equation:

(x + y) * 1/3 = 45,

x + y = 135,

x = 135 – y.

The first train travels the entire distance 9 minutes faster, which means:

45 / x = 45 / y + 3/20.

We substitute the value of x into this equation:

45 / (135 – y) = (900 + 3 * y) / 20 * y,

900 * y = 900 * 135 – 900 * y + 405 * y – 3 * y²,

– 3 * y² – 1395 * y + 121500 = 0.

The discriminant of this equation is:

(- 1395) ² – 4 * (-3) * 121500 = 3404025.

Since y can only be positive, the equation has a unique solution:

y = (1395 – 1845) / – 6 = 75 (km / h) – the speed of one train.

x = 135 – 75 = 60 (km / h) – the speed of the second train.