Question

Из двух пунктов реки, расстояние между которыми 51 км, навстречу друг другу движутся две моторные лодки, собствен¬ные скорости которых равны. Скорость течения реки 3 км/ч. Лодка, идущая по течению, до встречи прошла 1,5 ч, а лодка, идущая против течения, 2 ч. Найдите собственную скорость лодок.

Answer 1

Скорость лодки - х км/час,                             
скорость одной лодки которая идет по теч.- (х+3) км/час,    
скорость лодки , идущей против теч. - (х-3) км/час
1,5(х+3)+2(х-3)=51
1,5х+4,5+2х-6=51
3,5х=52,5
х=15 км/час - собственная скорость лодки

Answer 2

Problem Analysis

We have two motorboats moving towards each other on a river. The distance between them is 51 km. The speed of the river's current is 3 km/h. One boat, moving with the current, takes 1.5 hours to reach the other boat, while the other boat, moving against the current, takes 2 hours to reach the other boat. We need to find the speed of the motorboats.

Solution

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

When the boat is moving with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed of the boat moving with the current is (x + 3) km/h.

When the boat is moving against the current, its effective speed is the difference between its own speed and the speed of the current. Therefore, the effective speed of the boat moving against the current is (x - 3) km/h.

We can use the formula speed = distance / time to calculate the speed of each boat.

For the boat moving with the current: - Distance = 51 km - Time = 1.5 hours

For the boat moving against the current: - Distance = 51 km - Time = 2 hours

Let's calculate the speeds of the boats using the given information.

Calculation

For the boat moving with the current: - Speed = Distance / Time - Speed = 51 km / 1.5 hours - Speed = 34 km/h

For the boat moving against the current: - Speed = Distance / Time - Speed = 51 km / 2 hours - Speed = 25.5 km/h

Therefore, the speed of each motorboat is as follows: - The boat moving with the current has a speed of 34 km/h. - The boat moving against the current has a speed of 25.5 km/h.

Answer

The speed of the motorboats is as follows: - The boat moving with the current has a speed of 34 km/h. - The boat moving against the current has a speed of 25.5 km/h.