Two boats are moving towards each other. Now there are 25 km between them. The speed of one of them

Two boats are moving towards each other. Now there are 25 km between them. The speed of one of them is [seven-eighths] of the speed of the other. Find the speed of each boat if you know they will meet in [five-twelfth] hours.

1. Let’s designate the speed of the first boat as x km / h.

2. The speed of the second boat is 7/8 of the speed of the first, which means that the speed of the second boat is (7/8 * x) km / h.

3. Since the boats are moving towards each other, the speed of their approach is:

x + (7/8 * x) = 15/8 * x km / h.

4. By the condition of the problem, it is known that, moving towards each other, the boats will cover the distance of 25 km in 5/12 hours.

5. Hence, according to the formula of the path, the speed of approach of the boats is equal to the quotient of dividing the distance by time, ie. 25 / (5/12) = 25/5 * 12 = 60 km / h.

6. We get equality:

15/8 * x = 60;

15 * x = 60 * 8;

x = 480/15 = 32;

7. We got that the speed of the first boat is 32 km / h, which means that the speed of the second boat is 32 * 7/8 = 28 km / h.

Answer: the speed of one boat is 32 km / h, the speed of the other boat is 28 km / h.