Question

Поможіть з задачею- моторний човен проплив 42.75км за течією річки і 23.1 км проти.Скільки часу рухався човен,якщо його власна швидкість 32.5км за год,а швидкість за течією 34.2 км за год ?

Answer 1

34,2 - 32,5 = 1,7(км/ч) - скорость течения
32,5 - 1,7 =  30,8(км/ч) - скорость катера против течения
42,75 : 34,2 = 1,25 (ч) - плыл катер по течению
23,1 : 30,8 = 0,75(ч) - плыл катер против течения
1,25 + 0,75 = 2(ч) - время движения катера
Ответ: 2 часа

Answer 2

Problem Analysis

To solve this problem, we need to find the time it took for the boat to travel a certain distance both downstream and upstream. We are given the boat's own speed, the speed of the river current, and the distances traveled in each direction.

Downstream Speed

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. Therefore, the boat's speed downstream is calculated as follows: Downstream Speed = Boat's Own Speed + Speed of River Current

Upstream Speed

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. Therefore, the boat's speed upstream is calculated as follows: Upstream Speed = Boat's Own Speed - Speed of River Current

Time Calculation

To calculate the time it took for the boat to travel a certain distance, we can use the formula: Time = Distance / Speed

Solution

Let's calculate the time it took for the boat to travel downstream and upstream.

Downstream Time

Given: - Distance downstream = 42.75 km - Boat's own speed = 32.5 km/h - Speed of river current = 34.2 km/h

Using the formula for time, we can calculate the time it took for the boat to travel downstream: Downstream Time = Distance downstream / Downstream Speed

To calculate the downstream speed, we add the boat's own speed to the speed of the river current: Downstream Speed = Boat's Own Speed + Speed of River Current

Let's calculate the downstream time: Downstream Speed = 32.5 km/h + 34.2 km/h = 66.7 km/h Downstream Time = 42.75 km / 66.7 km/h = 0.640 hours

Therefore, it took the boat approximately 0.640 hours to travel downstream.

Upstream Time

Given: - Distance upstream = 23.1 km - Boat's own speed = 32.5 km/h - Speed of river current = 34.2 km/h

Using the formula for time, we can calculate the time it took for the boat to travel upstream: Upstream Time = Distance upstream / Upstream Speed

To calculate the upstream speed, we subtract the speed of the river current from the boat's own speed: Upstream Speed = Boat's Own Speed - Speed of River Current

Let's calculate the upstream time: Upstream Speed = 32.5 km/h - 34.2 km/h = -1.7 km/h **Upstream Time = 23.1