Question

Собственная скорость катера = 13 км/ч. За какое время катер пройдет 30 километров по течению реки. Обозначьте скорость течения буквой v и составьте выражения по условию задачи. Какая должна быть скорость течения реки, если известно, что катер пройдет 30 километров за два часа?

Answer 1

Ответ:

v(скорость)*t(время)= s(пройденное расстояние)

скорость течения прибавляется к скорости катера, если он идет по течению, и вычитается если против

(13+v)*2= 30

13+v = 15

v = 2

Answer 2

Ответ:

30 : 2=15км/ч-скорость катера по течению

V=15-13=2км/ч-скорость течения

Answer 3

Problem Analysis

We are given that the speed of the boat is 13 km/h. We need to find the time it takes for the boat to travel 30 kilometers downstream in a river. We are also asked to represent the speed of the current with the variable 'v' and write expressions based on the given conditions. Additionally, we need to determine the speed of the river current if we know that the boat can travel 30 kilometers in two hours.

Solution

Let's break down the problem step by step.

1. Finding the time it takes for the boat to travel 30 kilometers downstream: - Let's assume the speed of the river current is 'v' km/h. - The boat's speed relative to the ground is the sum of its own speed and the speed of the current: 13 km/h + v km/h. - The distance the boat travels downstream is 30 kilometers. - We can use the formula: time = distance / speed. - Therefore, the time it takes for the boat to travel 30 kilometers downstream is: time = 30 km / (13 km/h + v km/h).

2. Determining the speed of the river current if the boat can travel 30 kilometers in two hours: - We are given that the boat can travel 30 kilometers in two hours. - Using the formula: speed = distance / time, we can rearrange it to find the speed. - Therefore, the speed of the river current is: v = (30 km) / (2 hours - time taken by the boat to travel 30 km downstream).

Let's substitute the values and calculate the time it takes for the boat to travel 30 kilometers downstream and the speed of the river current.

Calculation

1. Finding the time it takes for the boat to travel 30 kilometers downstream: - Let's assume the speed of the river current is 'v' km/h. - The boat's speed relative to the ground is 13 km/h + v km/h. - The distance the boat travels downstream is 30 kilometers. - Therefore, the time it takes for the boat to travel 30 kilometers downstream is: time = 30 km / (13 km/h + v km/h).

2. Determining the speed of the river current if the boat can travel 30 kilometers in two hours: - We are given that the boat can travel 30 kilometers in two hours. - Therefore, the speed of the river current is: v = (30 km) / (2 hours - time taken by the boat to travel 30 km downstream).

Let's calculate the time it takes for the boat to travel 30 kilometers downstream and the speed of the river current.

Calculation

1. Finding the time it takes for the boat to travel 30 kilometers downstream: - Let's assume the speed of the river current is 'v' km/h. - The boat's speed relative to the ground is 13 km/h + v km/h. - The distance the boat travels downstream is 30 kilometers. - Therefore, the time it takes for the boat to travel 30 kilometers downstream is: time = 30 km / (13 km/h + v km/h).

Substituting the given values, we have: time = 30 km / (13 km/h + v km/h)

2. Determining the speed of the river current if the boat can travel 30 kilometers in two hours: - We are given that the boat can travel 30 kilometers in two hours. - Therefore, the speed of the river current is: **v = (