Question

От пристани а к пристани б, расстояние между которыми 10 км, вниз по течению реки отправился плот. Через некоторое время вслед за ним отправился катер, который догнал плот через 15 минут и тут же, не меняя своей скорости повернул обратно. Известно, что плот причалил к пристани б на 54 минуты позже, чем катер к пристани а. Найдите собственную скорость катера и время движения катера от пристани а, если скорость течения реки 2 км/ч, а собственная скорость катера больше 10 км/ч.

Answer 1

Решение прицеплено в картинке

Answer 2

Problem Analysis

We are given the following information: - The distance between two ports, A and B, is 10 km. - A raft started downstream from port A. - After some time, a motorboat started from port A and caught up with the raft in 15 minutes. - The motorboat immediately turned back without changing its speed. - It is known that the raft docked at port B 54 minutes later than the motorboat docked at port A. - The speed of the river current is 2 km/h. - The speed of the motorboat is greater than 10 km/h.

We need to find the speed of the motorboat and the time it took for the motorboat to travel from port A.

Solution

Let's assume the speed of the motorboat is v km/h.

Since the motorboat caught up with the raft in 15 minutes, the distance traveled by the motorboat in 15 minutes is the same as the distance traveled by the raft in that time. The distance traveled by the motorboat in 15 minutes is (v - 2) km.

The time it took for the motorboat to travel from port A to the point where it caught up with the raft is the same as the time it took for the raft to travel from that point to port B. Let's denote this time as t.

The distance traveled by the motorboat from port A to the point where it caught up with the raft is (v - 2) * t km.

The distance traveled by the raft from that point to port B is 10 - (v - 2) * t km.

We are given that the raft docked at port B 54 minutes later than the motorboat docked at port A. Therefore, the time it took for the raft to travel from that point to port B is t + 54 minutes.

We can set up the following equation based on the distances and speeds:

(v - 2) * t = 10 - (v - 2) * (t + 54)

Now, let's solve this equation to find the value of v and t.

Calculation

Expanding the equation, we get:

v * t - 2 * t = 10 - v * t + 2 * t + 108

Simplifying the equation, we get:

2 * v * t = 118

Dividing both sides of the equation by 2 * t, we get:

v = 118 / (2 * t)

Since the speed of the motorboat is greater than 10 km/h, we can assume that t > 0.

Let's substitute the value of v in terms of t into the equation:

118 / (2 * t) = 10 - 118 / (2 * t) + 2

Multiplying both sides of the equation by 2 * t, we get:

118 = (10 - 118) * 2 * t + 4 * t

Simplifying the equation, we get:

118 = -216 * t + 4 * t

Combining like terms, we get:

118 = -212 * t

Dividing both sides of the equation by -212, we get:

t = -118 / 212

Since time cannot be negative, we can conclude that there is no solution to this problem.

Therefore, there is no valid answer to this question.