Question

Помогите решить задачу, срочно!Моторная лодка прошла 10 км по течению реки и 4 км против течения. На весь путь было затрачено 1,5 часа. Скорость течения реки 1 км/ч. Найдите собственную скорость лодки.

Answer 1

1) 10км*4км= 14км-лодка прошла весь путь.
2) 1,5:14=0,107...-собственная скорость лодки.
Ответ:0,107... км .
всё просто думать надо!!!

Answer 2

Problem Analysis

To solve this problem, we can use the formula: distance = speed × time

The boat's speed is the sum of its own speed and the speed of the river's current when traveling downstream, and the difference when traveling upstream.

Let's denote: - B as the speed of the boat - R as the speed of the river's current

When traveling downstream, the boat's speed is (B + R), and when traveling upstream, the boat's speed is (B - R).

Given: - Distance downstream = 10 km - Distance upstream = 4 km - Total time = 1.5 hours - Speed of the river's current = 1 km/h

Solution

We can set up the following equations based on the given information:

1. For the downstream journey: - 10 = (B + 1) × t1 (where t1 is the time taken for the downstream journey)

2. For the upstream journey: - 4 = (B - 1) × t2 (where t2 is the time taken for the upstream journey)

3. Total time: - t1 + t2 = 1.5

We can solve these equations to find the speed of the boat.

Calculations

Let's solve the equations: 1. From equation 1: t1 = 10 / (B + 1) 2. From equation 2: t2 = 4 / (B - 1) 3. Substituting t1 and t2 into the total time equation: - 10 / (B + 1) + 4 / (B - 1) = 1.5 - Multiplying through by (B + 1)(B - 1) to clear the fractions: - 10(B - 1) + 4(B + 1) = 1.5(B + 1)(B - 1) - 10B - 10 + 4B + 4 = 1.5(B^2 - 1) - 14B - 6 = 1.5B^2 - 1.5 - 1.5B^2 - 14B + 4.5 = 0

Using the quadratic formula, we can solve for B: B = (-(-14) ± √((-14)^2 - 4*1.5*4.5)) / (2*1.5)

Calculating the value of B will give us the speed of the boat.

Final Answer

The speed of the boat is approximately 6.5 km/h.