Question

Катер проплыл 72 км по течению за 2 ч,а против течения за 3 ч.За сколько часов это расстояние проплывут плоты? Даю 10 балов

Answer 1

Х  км/ч - скорость катера
у км/ч - скорость течения

2*(х+у)=72
3*(х-у)=72

х+у=36
х-у=24

х=36-у
36-у-у=24

х=36-у
2у=36-24

х=36-у
у=12:2

у=6(км/ч) - скорость течения
х=30(км/ч) - скорость катера.

Плот может плыть только ПО течению реки.
72:6=12(ч) - потребуется плотам 

Answer 2

По течению 36 часов , против течения 24 часа

Answer 3

Problem Analysis

We are given that a boat traveled 72 km downstream in 2 hours and the same distance upstream in 3 hours. We need to determine how long it will take for rafts to cover the same distance.

Downstream Speed

To find the speed of the boat downstream, we can divide the distance traveled by the time taken. In this case, the boat traveled 72 km downstream in 2 hours, so the downstream speed is 72 km/2 hours = 36 km/h.

Upstream Speed

Similarly, to find the speed of the boat upstream, we divide the distance traveled by the time taken. In this case, the boat traveled 72 km upstream in 3 hours, so the upstream speed is 72 km/3 hours = 24 km/h.

Relative Speed of the Rafts

When the boat is traveling downstream, it is aided by the current, which increases its effective speed. When the boat is traveling upstream, it is hindered by the current, which decreases its effective speed. The difference between the downstream and upstream speeds gives us the speed of the current.

The speed of the current can be calculated by taking the difference between the downstream and upstream speeds. In this case, the downstream speed is 36 km/h and the upstream speed is 24 km/h, so the speed of the current is 36 km/h - 24 km/h = 12 km/h.

Time for the Rafts to Cover the Distance

To determine how long it will take for the rafts to cover the same distance, we need to consider the relative speed of the rafts with respect to the current. The rafts will be traveling at the same speed as the boat when going downstream and at the same speed as the current when going upstream.

When the rafts are traveling downstream, their speed will be the sum of the downstream speed of the boat and the speed of the current. In this case, the downstream speed of the boat is 36 km/h and the speed of the current is 12 km/h, so the speed of the rafts downstream is 36 km/h + 12 km/h = 48 km/h.

When the rafts are traveling upstream, their speed will be the difference between the upstream speed of the boat and the speed of the current. In this case, the upstream speed of the boat is 24 km/h and the speed of the current is 12 km/h, so the speed of the rafts upstream is 24 km/h - 12 km/h = 12 km/h.

To find the time it takes for the rafts to cover the distance, we divide the distance by the speed. In this case, the distance is 72 km.

- Time for the rafts to cover the distance downstream: 72 km / 48 km/h = 1.5 hours - Time for the rafts to cover the distance upstream: 72 km / 12 km/h = 6 hours

Therefore, the rafts will take 1.5 hours to cover the distance downstream and 6 hours to cover the distance upstream.

Answer

The rafts will take 1.5 hours to cover the distance downstream and 6 hours to cover the distance upstream.