Question

Теплоход проходит по течению реки до пункта назначения 16 км и после стоянки возвращается в пункт отправления. Найдите скорость теплохода в неподвижной воле, если скорость течения равна 4 км/ч, стоянка длится 5 часов, а в пункт отправления теплоход возвращается через 18 часов после отплытия из него.

Answer 1

Problem Analysis

We are given the following information: - The distance from the starting point to the destination is 16 km. - The speed of the current is 4 km/h. - The duration of the stop at the destination is 5 hours. - The return trip from the destination to the starting point takes 18 hours.

We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is v km/h.

When the boat is moving downstream (towards the destination), the effective speed of the boat is the sum of its speed in still water and the speed of the current. Therefore, the effective speed is v + 4 km/h.

When the boat is moving upstream (returning to the starting point), the effective speed of the boat is the difference between its speed in still water and the speed of the current. Therefore, the effective speed is v - 4 km/h.

We can use the formula distance = speed × time to calculate the distance traveled in each direction.

Let's calculate the distance traveled downstream and upstream:

- Downstream distance: (v + 4) × (16 km) - Upstream distance: (v - 4) × (16 km)

Since the boat returns to the starting point after 18 hours, the total time spent traveling upstream and downstream is 18 hours.

We can set up the following equation to solve for v:

Downstream distance + Upstream distance = 16 km

[(v + 4) × (16 km)] + [(v - 4) × (16 km)] = 16 km

Simplifying the equation:

32v = 16 km

v = (16 km) / 32

v = 0.5 km/h

Therefore, the speed of the boat in still water is 0.5 km/h.

Answer

The speed of the boat in still water is 0.5 km/h.