Question

По течению реки катер прошел за 7 столько же , сколько он проходит за 8 ч против течения . Собственная скорость катера 30 км /ч . Сколько километров проплывает за 4 ч спичка , брошенная в эту реку

Answer 1

[-скорость реки,х+30-скорость по течению, 30-х-скорость против течения
7(30+х)=8(30-х)
210+7х=240-8х
7х+8х=240-210
15х=30
х=30/15=2км\ч скорость течения
2*4=8км проплывет спичка.

Answer 2

Calculation of the Boat's Speed

To solve this problem, we need to determine the speed of the boat relative to the water and the speed of the river's current. Let's break down the given information:

- The boat travels a certain distance in 7 hours downstream (with the current). - The boat travels the same distance in 8 hours upstream (against the current). - The boat's own speed is 30 km/h.

Let's denote the speed of the boat relative to the water as v and the speed of the river's current as c.

1. Downstream speed: When the boat is moving downstream, its speed is increased by the speed of the current. Therefore, the effective speed of the boat is v + c. 2. Upstream speed: When the boat is moving upstream, its speed is decreased by the speed of the current. Therefore, the effective speed of the boat is v - c.

According to the given information, the boat travels the same distance in both cases. We can set up the following equation:

Distance = Speed × Time

Let's calculate the distance traveled downstream and upstream:

1. Downstream distance: The boat travels a certain distance in 7 hours downstream. Therefore, the distance traveled downstream is (v + c) × 7. 2. Upstream distance: The boat travels the same distance in 8 hours upstream. Therefore, the distance traveled upstream is (v - c) × 8.

Since the distances are the same, we can set up the equation:

(v + c) × 7 = (v - c) × 8

Now, let's solve this equation to find the values of v and c.

Solving the Equation

To solve the equation, we can start by expanding it:

7v + 7c = 8v - 8c

Next, let's group the variables on one side and the constants on the other side:

7v - 8v = 8c - 7c

Simplifying further:

-v = c

From this equation, we can see that the speed of the boat relative to the water (v) is equal to the speed of the river's current (c), but in the opposite direction.

Calculating the Distance Traveled in 4 Hours

Now that we know the speed of the boat relative to the water is 30 km/h and the speed of the river's current is also 30 km/h, we can calculate the distance traveled in 4 hours.

The boat's speed relative to the water is v = 30 km/h and the speed of the river's current is c = 30 km/h.

1. Downstream distance: The boat's effective speed downstream is (v + c) = (30 + 30) = 60 km/h. Therefore, the distance traveled downstream in 4 hours is 60 km/h × 4 h = 240 km.

Therefore, the boat will travel 240 kilometers in 4 hours downstream.

Conclusion

In summary, the boat will travel 240 kilometers in 4 hours downstream when it is thrown into the river with a speed of 30 km/h and the river's current is also 30 km/h.

Please note that the calculations and conclusions are based on the given information and assumptions made.