Question

Моторная лодка преодолела расстояние за течением реки 12 км и вернулпсь обратно за 2.5 часа. Потом эта же моторная лодка за 1 час 20 мин преодолела за течением реки 4 км, а против течения 8. Найдите скорость лодки и течения

Answer 1

Х скорость лодки        у скорость течения
12/(х+у)+12/(х-у)=2,5
4/(х+у)+8(х-у)=1 1/3
решение системы на картинке, решал, как мне удобно

Answer 2

Problem Analysis

We are given the following information about a motorboat's journey: - The boat traveled a distance of 12 km downstream and returned in 2.5 hours. - The boat traveled a distance of 4 km downstream in 1 hour and 20 minutes. - The boat traveled a distance of 8 km upstream in the same amount of time.

We need to find the speed of the boat and the speed of the current.

Downstream Journey

Let's start by calculating the speed of the boat during the downstream journey. We know that the boat traveled a distance of 12 km downstream and returned in 2.5 hours. To find the speed, we can use the formula:

Speed = Distance / Time

The speed of the boat during the downstream journey is given by:

Speed_downstream = 12 km / 2.5 hours

Upstream Journey

Next, let's calculate the speed of the boat during the upstream journey. We know that the boat traveled a distance of 8 km upstream in the same amount of time it took to travel 4 km downstream (1 hour and 20 minutes). To find the speed, we can again use the formula:

Speed = Distance / Time

The speed of the boat during the upstream journey is given by:

Speed_upstream = 8 km / 1.33 hours

Boat Speed and Current Speed

Let's assume the speed of the boat is represented by 'B' and the speed of the current is represented by 'C'. The speed of the boat relative to the ground during the downstream journey is the sum of the boat speed and the current speed, while the speed of the boat relative to the ground during the upstream journey is the difference between the boat speed and the current speed.

Using this information, we can set up the following equations:

Speed_downstream = B + C

Speed_upstream = B - C

We can solve these equations to find the values of B (boat speed) and C (current speed).

Solution

Let's calculate the boat speed and current speed using the given information.

Speed_downstream = 12 km / 2.5 hours = 4.8 km/h Speed_upstream = 8 km / 1.33 hours = 6.02 km/h Now, let's solve the equations:

4.8 km/h = B + C

6.02 km/h = B - C

Adding the two equations together, we get:

4.8 km/h + 6.02 km/h = 2B

Simplifying, we find:

10.82 km/h = 2B

Dividing both sides by 2, we get:

B = 5.41 km/h

Substituting the value of B into one of the equations, we can solve for C:

4.8 km/h = 5.41 km/h + C

Simplifying, we find:

C = -0.61 km/h

Answer

The speed of the boat is 5.41 km/h and the speed of the current is -0.61 km/h (which indicates that the current is flowing in the opposite direction of the boat).