Question

оторная лодка плыла 3 часа по течению реки и 7 часов против течения, пройдя за это время 124 км. Найдите собственную скорость лодки, если скорость течения реки 4 км/ч.

Answer 1

Problem Analysis

We are given that a boat traveled for 3 hours with the current and 7 hours against the current, covering a total distance of 124 km. The speed of the river current is given as 4 km/h. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat is x km/h.

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed is (x + 4) km/h.

When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed is (x - 4) km/h.

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

1. When the boat is traveling with the current: - Speed = (x + 4) km/h - Time = 3 hours - Distance = (x + 4) × 3 km

2. When the boat is traveling against the current: - Speed = (x - 4) km/h - Time = 7 hours - Distance = (x - 4) × 7 km

According to the problem, the total distance covered is 124 km. So, we can set up the equation:

(x + 4) × 3 + (x - 4) × 7 = 124

Simplifying the equation:

3x + 12 + 7x - 28 = 124

10x - 16 = 124

10x = 140

x = 14

Therefore, the speed of the boat is 14 km/h.

Answer

The speed of the boat is 14 km/h.