Question

Моторная лодка,двигаясь против течения реки,проплыла расстояние за 3 часа,а обратно за 2 часа 15 минут, Скорость течения реки 4 км/ч, Какова собственная скорость лодки?

Answer 1

Пусть скорость движения лодки 5 км/ч, а скорость течения - 2 км/ч.
1) 5 + 2= 7 (км/ч) - скорость лодки по течению
2) 5 - 2 = 3 (км/ч) - скорость лодки против течения

Пусть наша лодка проплыла 2 часа по течению реки и 3 часа против течения реки. Найдем расстояние, которое проплывет лодка.
3) 7 ∙ 2 = 14 (км) - плыла лодка по течению
4) 3 ∙ 3 = 9 (км) - плыла лодка против течения
5) 14 + 9 = 23 (км) - все расстояние
Ответ: 23 км.

Answer 2

Calculation of the Boat's Speed

To determine the boat's speed, we need to consider the time it took for the boat to travel both upstream (against the current) and downstream (with the current) on the river.

Let's denote the boat's speed as x km/h and the speed of the river's current as 4 km/h.

Given that the boat took 3 hours to travel upstream and 2 hours 15 minutes (or 2.25 hours) to travel downstream, we can set up the following equations:

1. Upstream: Distance = Speed x Time - Distance = 3x km - Time = 3 hours

2. Downstream: Distance = Speed x Time - Distance = (x + 4) km - Time = 2.25 hours

To solve for x, we can equate the distances traveled upstream and downstream:

3x = (x + 4) x 2.25

Simplifying the equation:

3x = 2.25x + 9

3x - 2.25x = 9

0.75x = 9

x = 9 / 0.75

x = 12

Therefore, the boat's own speed is 12 km/h.

Answer

The boat's own speed is 12 km/h.