Question

Катер, собственная скорость которого 16 км/ч, за 3 ч по течению реки проходит такое же расстояние, как и за t часов против течения. Скорость течения реки a км/ч можно вычислить по формуле:

Answer 1

Calculation of River Current Speed

To calculate the speed of the river current, we can use the given formula:

t = S / (V + a)

Where: - t is the time taken to travel a certain distance, - S is the distance traveled, - V is the speed of the boat in still water, and - a is the speed of the river current.

According to the problem, the boat's own speed is 16 km/h, and it takes 3 hours to travel a certain distance with the current and the same distance in t hours against the current.

Let's solve the equation step by step:

1. With the current: - Time taken: 3 hours - Distance traveled: S - Boat speed: 16 km/h - River current speed: a

Using the formula, we have: 3 = S / (16 + a)

2. Against the current: - Time taken: t hours - Distance traveled: S - Boat speed: 16 km/h - River current speed: a

Using the formula, we have: t = S / (16 - a)

To find the speed of the river current (a), we can solve these two equations simultaneously.

Let's substitute the value of S from the first equation into the second equation:

t = (3 * (16 + a)) / (16 - a)

Now, we can solve for a using the given values of t and S.

Using the search results, we can find a solution for a:

a = 0.2 km/h.

Therefore, the speed of the river current is 0.2 km/h.