Question

По течению реки катер проходит 28км за 1ч 20мин, а против течения - 24км за 1,5ч. Найти скорость течения реки

Answer 1

Пусть х(км/ч) -скорость течения реки.

у(км/ч) -собственная скорость катера.

Тогда скорость катера по течению реки равна (х+у) км/ч,

а против течения (у-х) км/ч. 

По условию по течению катер прошел 28 (км), т.е. 5/3 х +5/3 у(км),  

а против течения 24(км), т. е. 1,5 у -1,5 х (км).

(5/3 - это 1час  20мин.)

 5/3 х +5/3 у =28 домножим на  3

1,5 у-1,5 х=24  домножим  на 10

 5х+5у=84

15у-15х=240   разделим на 3

 5х+5у=84

 5у-5х=80

Решим систему  способом сложения двух уравнений:

 10у = 164

 5у-5х = 80

 

5у - 5х = 80

у = 16,4

 

5*16,4 - 5х = 80

у=16,4

 

-5 х = 80-82

у = 16,4

 

-5 х = -2

у = 16,4

 

х = 0,4

у = 16,4

Ответ:  0,4 (км/ч) -  скорость течения реки

Answer 2

Problem Analysis

We are given the information that a boat travels 28 km downstream in 1 hour and 20 minutes, and 24 km upstream in 1.5 hours. We need to find the speed of the river's current.

Downstream Speed Calculation

To find the speed of the boat in still water, we can use the formula:

Boat speed in still water = (Downstream speed + Upstream speed) / 2

Let's calculate the downstream speed of the boat first. We are given that the boat travels 28 km downstream in 1 hour and 20 minutes. We need to convert the time to hours.

1 hour and 20 minutes is equal to 1.33 hours (since 1 hour = 60 minutes).

Now, we can calculate the downstream speed:

Downstream speed = Distance / Time

Downstream speed = 28 km / 1.33 hours

Upstream Speed Calculation

Next, let's calculate the upstream speed of the boat. We are given that the boat travels 24 km upstream in 1.5 hours.

Upstream speed = Distance / Time

Upstream speed = 24 km / 1.5 hours

Boat Speed in Still Water Calculation

Now that we have the downstream and upstream speeds, we can calculate the boat's speed in still water using the formula mentioned earlier:

Boat speed in still water = (Downstream speed + Upstream speed) / 2

Calculation

Let's calculate the downstream speed, upstream speed, and the boat's speed in still water.

Downstream speed = 28 km / 1.33 hours = 21.05 km/h

Upstream speed = 24 km / 1.5 hours = 16 km/h

Boat speed in still water = (21.05 km/h + 16 km/h) / 2 = 18.53 km/h

Calculation of River's Current Speed

To find the speed of the river's current, we can subtract the boat's speed in still water from the downstream speed or the upstream speed. Since the downstream speed is higher, we will subtract the boat's speed in still water from the downstream speed.

River's current speed = Downstream speed - Boat speed in still water

River's current speed = 21.05 km/h - 18.53 km/h

Answer

The speed of the river's current is approximately 2.52 km/h.