Question

Лодка проплыла некоторое расстояние от пристани по течению реки и вернулась обратно, затратив на весь путь 8 ч. Собственная скорость лодки 8 км/ч, а скорость течения реки 2 км/ч. Определите,сколько времени плыла лодка по течению реки и все расстояние,которое она проплыла

Answer 1

Обозначим расстояние, пройденное лодкой в одну сторону = х.Тогда имеем:(х/10) + (х/6) = 8 (10 это скорость лодки при ее ходе по течению)(6 - это скорость лодки при ее ходе против течения) Решая уравнение, получаем: х=30. Общее расстояние, пройденное лодкой = 30*2=60

Answer 2

Problem Analysis

We are given the following information: - The boat's own speed is 8 km/h. - The speed of the river's current is 2 km/h. - The boat traveled a certain distance downstream and then returned, taking a total of 8 hours for the entire trip.

We need to determine: 1. How much time the boat spent traveling downstream. 2. The total distance the boat traveled.

Solution

Let's assume that the boat traveled a certain distance downstream in time `t1` and then returned the same distance upstream in time `t2`. We can use the formula `distance = speed * time` to calculate the distances traveled.

1. Calculating the time spent traveling downstream: - The boat's speed relative to the water is the sum of its own speed and the speed of the river's current: `8 km/h + 2 km/h = 10 km/h`. - The distance traveled downstream is equal to the boat's speed relative to the water multiplied by the time spent traveling downstream: `distance = 10 km/h * t1`. - We know that the boat traveled the same distance upstream, so the time spent traveling upstream is also `t1`. - The total time for the entire trip is given as 8 hours, so we can write the equation: `t1 + t2 = 8 hours`. - We can solve this equation to find the value of `t1`.

2. Calculating the total distance traveled: - The total distance traveled is the sum of the distance traveled downstream and the distance traveled upstream: `total distance = distance downstream + distance upstream`. - Using the formula `distance = speed * time`, we can calculate the distances traveled: `distance downstream = 10 km/h * t1` and `distance upstream = 8 km/h * t2`. - We can substitute the value of `t1` from the previous step into the equation to find the total distance traveled.

Let's calculate the values step by step.

Calculation

1. Calculating the time spent traveling downstream: - Let's assume the time spent traveling downstream is `t1` hours. - The time spent traveling upstream is also `t1` hours. - The total time for the entire trip is given as 8 hours, so we can write the equation: `t1 + t1 = 8 hours`. - Simplifying the equation: `2t1 = 8 hours`. - Solving for `t1`: `t1 = 8 hours / 2 = 4 hours`.

2. Calculating the total distance traveled: - The distance traveled downstream is equal to the boat's speed relative to the water multiplied by the time spent traveling downstream: `distance downstream = 10 km/h * 4 hours = 40 km`. - The distance traveled upstream is equal to the boat's own speed multiplied by the time spent traveling upstream: `distance upstream = 8 km/h * 4 hours = 32 km`. - The total distance traveled is the sum of the distance downstream and the distance upstream: `total distance = 40 km + 32 km = 72 km`.

Answer

The boat spent 4 hours traveling downstream and the total distance it traveled was 72 km.