Question

От пристани по реке отправился плот(!). Через 3/4ч вслед за ним вышла лодка и через 0,75ч обогнала плот на 9,6 км. Найдите собственную скорость лодки, если скорость течения реки равна 2 км/ч.

Answer 1

Скорость плота = скорости течения реки = 2 км/ч
1) 2 * 3/4 = 1,5 км проплыл плот за 3/4 часа
2) 1,5 + 9,6 = 11,1 км - проплыла лодка
3) 11,1 : 0,75 = 14,8 км/ч - скорость лодки по течению реки
4) 14,8 - 2 = 12,8 км/ч - собственная скорость лодки

Answer 2

Problem Analysis

We are given that a raft (плот) started from a dock on a river, and after 3/4 of an hour, a boat (лодка) started from the same dock. The boat caught up with the raft after 0.75 hours and traveled a distance of 9.6 km. We need to find the speed of the boat, given that the speed of the river current is 2 km/h.

Solution

Let's assume the speed of the boat is B km/h and the speed of the raft is R km/h.

We know that the boat caught up with the raft after 0.75 hours and traveled a distance of 9.6 km. This means that the boat's speed relative to the raft is 9.6 km / 0.75 h = 12.8 km/h.

Since the boat is moving against the current, its effective speed is reduced by the speed of the current. So, the boat's speed relative to the ground is B - 2 km/h.

Similarly, the raft is also moving against the current, so its effective speed relative to the ground is R - 2 km/h.

Since the boat caught up with the raft, their relative speeds must be equal. Therefore, we can set up the following equation:

B - 2 = 12.8

Solving this equation will give us the speed of the boat, B.

Let's solve the equation:

B - 2 = 12.8

Adding 2 to both sides:

B = 12.8 + 2

B = 14.8

Therefore, the speed of the boat is 14.8 km/h.

Answer

The speed of the boat is 14.8 km/h.