Question

Мальчик проплыл некоторое расстояние по течению реки за 24 с и это же расстояние против течения за 40 с. Определи собственную скорость пловца, считая её постоянной от начала и до конца заплыва, если скорость течения реки 15м/мин.

Answer 1

Пусть собственная скорость пловца равна х м/мин, тогда скорость по течению равна (х+15) м/мин, а скорость против течения - (х-15) м/мин. Некоторое расстояние по течению он проплыл за 24 с = 0,4 мин, значит он проплыл: 0,4*(х+15) м, а против течения - за 40 с = 2/3 мин, значит, он проплыл 2/3*(x-15) м.
По условию известно, что и по течению, и против течения мальчик проплыл одинаковое расстояние, поэтому составим уравнение:

0,4*(x+15) = 2/3*(x-15)
0,4x + 6 = 2/3x - 10
2/5x + 6 - 2/3x + 10 = 0
6/15x - 10/15x + 16 = 0
-4/15x + 16 = 0
-4/15x = -16
4/15x = 16
x = 16 : 4/15
x = 16 * 15/4
x = 60 (м/мин) - скорость пловца

ОТВЕТ: 60 м/мин

Answer 2

Problem Analysis

We are given that a boy swims a certain distance downstream in 24 seconds and the same distance upstream in 40 seconds. We need to determine the swimmer's own speed, assuming it is constant throughout the swim, given that the river's current speed is 15 m/min.

Solution

Let's assume the distance the boy swims is d.

When swimming downstream, the swimmer's effective speed is the sum of his own speed and the current speed. Therefore, the time taken to swim downstream is given by:

d = (swimmer's speed + current speed) * time

Substituting the given values, we have:

d = (swimmer's speed + 15 m/min) * 24 s

Similarly, when swimming upstream, the swimmer's effective speed is the difference between his own speed and the current speed. Therefore, the time taken to swim upstream is given by:

d = (swimmer's speed - current speed) * time

Substituting the given values, we have:

d = (swimmer's speed - 15 m/min) * 40 s

We can solve these two equations simultaneously to find the swimmer's own speed.

Let's solve the equations:

d = (swimmer's speed + 15 m/min) * 24 s

d = (swimmer's speed - 15 m/min) * 40 s

Expanding the equations:

24s * swimmer's speed + 360s = 40s * swimmer's speed - 600s

Rearranging the equation:

16s * swimmer's speed = 960s

Dividing both sides by 16s:

swimmer's speed = 60 m/min

Therefore, the swimmer's own speed is 60 m/min.

Answer

The swimmer's own speed is 60 m/min.