Question

Из двух пунктов реки навстречу друг другу движутся две моторные лодки , собственные скорости которых равны.до встречи лодка,идущая по течению ,шла 1,1 часа,а лодка, идущая против течения , 1,5 часа.найдите собственную скорость лодок, если лодка, идущая по течению реки, до встречи прошла на 1 км больше другой лодки.скорость течения реки 3 км/ч

Answer 1

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Answer 2

Problem Analysis

We are given two motorboats moving towards each other in a river. The boats have the same speed, and we need to find their individual speeds. We are also given that the boat moving with the current traveled for 1.1 hours, while the boat moving against the current traveled for 1.5 hours. Additionally, the boat moving with the current traveled 1 km more than the other boat before they met. The speed of the river current is given as 3 km/h.

To solve this problem, we can set up a system of equations based on the given information and solve for the unknown speeds of the boats.

Solution

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

1. We can calculate the distance traveled by the boat moving with the current using the formula: - Distance = Speed × Time - Distance = V × 1.1

2. We can calculate the distance traveled by the boat moving against the current using the same formula: - Distance = Speed × Time - Distance = V × 1.5

3. We are given that the boat moving with the current traveled 1 km more than the other boat before they met. So we can set up the following equation: - Distance of boat moving with the current = Distance of boat moving against the current + 1 - V × 1.1 = V × 1.5 + 1

Now, let's solve this equation to find the value of V.

Calculation

Using the equation V × 1.1 = V × 1.5 + 1, we can solve for V:

1.1V = 1.5V + 1 0.4V = 1 V = 1 / 0.4 V = 2.5

Therefore, the speed of each boat is 2.5 km/h.

Answer

The speed of each boat is 2.5 km/h.