A motor boat travels 30 km from one pier to another in 6 hours along the river and in 10 hours

A motor boat travels 30 km from one pier to another in 6 hours along the river and in 10 hours against the river in how long will it take the same distance across the lake?

Decision.
Let the speed of a motor boat in still water or the boat’s own speed be x km / h, and the speed of the river will be y km / h. Then the boat speed along the river will be (x + y) km / h, and against the river (x – y) km / h. On the other hand, from the condition of the problem it is known that the distance of 30 km from one pier to another, the motor boat passes in 6 hours along the river, and in 10 hours against the river. That is, the speed of the boat along the river will be 30: 6 = 5 km / h, and against the river, 30: 10 = 3 km / h. Knowing this, we compose a system of two equations with two unknowns:
x + y = 5 and x – y = 3.
Let’s solve the system by the addition method, adding the left and right sides of the equation term by term:
x + y + x – y = 5 + 3;
2 ∙ x = 8;
x = 8: 2;
x = 4 (km / h) – speed of a motor boat in still water.
To find out how long it will take it to travel the same distance across the lake, we divide the path by the speed of a motorboat in still water:
30: 4 = 7.5 (h).
Answer: a motor boat will cover the same distance across the lake in 7.5 hours.