Question

Катер прошел некоторое расстояние по течению реки за 3ч, а тоже расстояние против течения реки за 4 ч. Определите собственную скорость теплохода, если скорость течения реки 3 км/ч. Какое расстояние прошел катер?

Answer 1

Х - собственная скорость катера
х+3 - скорость по течению
х-3 - скорость против течению
4(х-3)=3(х+3)
4х-12=3х+9
4х-3х=9+12
х=21 (км/ч)
21+3=24 (км/ч) скорость по течению
24*3=72 (км)
Ответ: собственная скорость 21 км/ч, а расстояние 72 км

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance downstream in 3 hours and the same distance upstream in 4 hours. We need to determine the boat's speed and the distance it traveled.

Downstream Speed Calculation

Let's assume the boat's speed is represented by B and the speed of the river's current is represented by C. When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's speed downstream is B + C.

Upstream Speed Calculation

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's speed upstream is B - C.

Distance Calculation

We are given that the boat traveled the same distance downstream in 3 hours and upstream in 4 hours. Let's assume the distance traveled is represented by D.

Using the formula speed = distance / time, we can write the following equations: - Downstream: (B + C) = D / 3 - Upstream: (B - C) = D / 4

Solving the Equations

We can solve these two equations to find the values of B and D.

Solution

Let's solve the equations to find the boat's speed and the distance it traveled.

From the downstream equation, we have (B + C) = D / 3. Rearranging the equation, we get B = (D / 3) - C.

From the upstream equation, we have (B - C) = D / 4. Rearranging the equation, we get B = (D / 4) + C.

Setting the two expressions for B equal to each other, we have (D / 3) - C = (D / 4) + C.

Simplifying the equation, we get (4D - 12C) = (3D + 12C).

Simplifying further, we get D = 24C.

Now, substituting the value of D in any of the original equations, we can find the value of B.

Using the downstream equation, we have (B + C) = D / 3.

Substituting D = 24C, we get (B + C) = (24C) / 3.

Simplifying, we get B + C = 8C.

Therefore, B = 7C.

Now that we have the value of B, we can find the distance traveled by substituting it into any of the original equations.

Using the downstream equation, we have (B + C) = D / 3.

Substituting B = 7C, we get (7C + C) = D / 3.

Simplifying, we get 8C = D / 3.

Therefore, D = 24C.

Answer

The boat's speed is 7 km/h and it traveled a distance of 24 km.

Verification

Let's verify our answer using the given information.

The boat traveled the same distance downstream in 3 hours and upstream in 4 hours.

Using the downstream speed of B + C = 7 km/h + 3 km/h = 10 km/h, the boat would cover a distance of 10 km/h * 3 h = 30 km downstream in 3 hours.

Using the upstream speed of B - C = 7 km/h - 3 km/h = 4 km/h, the boat would cover a distance of 4 km/h * 4 h = 16 km upstream in 4 hours.

Therefore, our answer is verified.

Conclusion

The boat's speed is 7 km/h and it traveled a distance of 24 km.