Question

Между пристанями 40 км. Моторная лодка прошла этот путь по течению реки за 2 ч, против течения реки-за 4 ч. Какова скорость течения реки? Подскажите решение пожалуйста.

Answer 1

Скорость у моторной 20 км/ч,20*2= 40 км.
40/10=10 км/ч скорость против течения,
20-10=10 км/ч скорость реки,мы из первоначальной скорости моторной лодки по течению вычитаем скорость моторной лодки против течения и получается скорость течения реки. 

Answer 2

Problem Analysis

We are given that a motorboat traveled a distance of 40 km between two piers. The boat traveled this distance downstream in 2 hours and upstream in 4 hours. We need to find the speed of the river's current.

Solution

Let's assume the speed of the boat in still water is B km/h, and the speed of the river's current is C km/h.

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the boat's speed downstream is B + C km/h.

When the boat is traveling upstream (against the current), its effective speed is decreased by the speed of the current. Therefore, the boat's speed upstream is B - C km/h.

We can use the formula distance = speed × time to set up two equations based on the given information:

1. When traveling downstream: 40 = (B + C) × 2 2. When traveling upstream: 40 = (B - C) × 4

We can solve this system of equations to find the values of B and C.

Solving the Equations

Let's solve the system of equations using the substitution method.

From equation 1, we have 40 = (B + C) × 2. Simplifying, we get 20 = B + C.

We can rewrite equation 2 as 40 = (B - C) × 4. Simplifying, we get 10 = B - C.

Now we have a system of equations: - Equation A: 20 = B + C - Equation B: 10 = B - C

We can solve this system by adding equations A and B together:

(20 + 10) = (B + C) + (B - C)

Simplifying, we get 30 = 2B.

Dividing both sides by 2, we find B = 15.

Now that we have the value of B, we can substitute it back into equation A to find the value of C:

20 = 15 + C

Simplifying, we find C = 5.

Answer

The speed of the river's current is 5 km/h.

Verification

Let's verify our answer by substituting the values of B and C back into the original equations:

1. When traveling downstream: 40 = (15 + 5) × 2. Simplifying, we get 40 = 20 × 2, which is true. 2. When traveling upstream: 40 = (15 - 5) × 4. Simplifying, we get 40 = 10 × 4, which is also true.

Therefore, our answer of C = 5 km/h is correct.

Answer 3

Problem Analysis

We are given that a motorboat traveled a distance of 40 km between two piers. It took 2 hours to travel this distance downstream (with the current) and 4 hours to travel the same distance upstream (against the current). We need to find the speed of the river's current.

Solution

Let's assume the speed of the motorboat in still water is B km/h, and the speed of the river's current is C km/h.

When the motorboat is traveling downstream (with the current), the effective speed of the motorboat is the sum of its speed in still water and the speed of the current. Therefore, the effective speed is B + C km/h.

When the motorboat is traveling upstream (against the current), the effective speed of the motorboat is the difference between its speed in still water and the speed of the current. Therefore, the effective speed is B - C km/h.

We can use the formula distance = speed × time to calculate the distances traveled in each case.

Downstream Travel

The distance traveled downstream is 40 km, and the time taken is 2 hours. Using the formula distance = speed × time, we can write the equation:

40 = (B + C) × 2.

Upstream Travel

The distance traveled upstream is also 40 km, but the time taken is 4 hours. Using the formula distance = speed × time, we can write the equation:

40 = (B - C) × 4.

Now we have a system of two equations with two variables (B and C). We can solve this system of equations to find the values of B and C.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From the equation 40 = (B + C) × 2, we can rewrite it as B + C = 20.

From the equation 40 = (B - C) × 4, we can rewrite it as B - C = 10.

Now we have a system of equations:

B + C = 20 (Equation 1)

B - C = 10 (Equation 2)

We can solve this system of equations by adding Equation 1 and Equation 2:

(B + C) + (B - C) = 20 + 10

Simplifying, we get:

2B = 30

Dividing both sides by 2, we find:

B = 15

Now that we have the value of B, we can substitute it back into Equation 1 to find the value of C:

15 + C = 20

Subtracting 15 from both sides, we get:

C = 5

Therefore, the speed of the river's current is 5 km/h.

Answer

The speed of the river's current is 5 km/h.