Question

Моторная лодка собственная скорость которой равна 21 км/ч отправилась из города А по течению реки, скорость которой равна 3 км/ч , в город В. Остановившись в городе В на 7 часов,лодка отправилась обратно в город А. На весь путь было потрачено 35 часов.Сколько километров прошла лодка ?​

Answer 1

Смотри.................

Answer 2

Problem Analysis

We are given the following information: - The speed of a motorboat is 21 km/h. - The speed of the river current is 3 km/h. - The boat stops in city B for 7 hours. - The total time for the round trip is 35 hours.

We need to determine the distance traveled by the boat.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's break down the problem into two parts: the downstream journey from city A to city B, and the upstream journey from city B back to city A.

# Downstream Journey

During the downstream journey, the boat is moving in the same direction as the river current. So, the effective speed of the boat is the sum of its own speed and the speed of the river current.

Let's denote the distance between city A and city B as d1.

The time taken for the downstream journey can be calculated using the formula: time = distance / speed.

The time taken for the downstream journey is given by: time1 = d1 / (21 + 3).

# Upstream Journey

During the upstream journey, the boat is moving against the river current. So, the effective speed of the boat is the difference between its own speed and the speed of the river current.

Let's denote the distance between city B and city A as d2.

The time taken for the upstream journey can be calculated using the formula: time = distance / speed.

The time taken for the upstream journey is given by: time2 = d2 / (21 - 3).

# Total Time

The total time for the round trip is given as 35 hours.

We can write the equation: time1 + time2 + 7 = 35.

Simplifying the equation, we get: d1 / 24 + d2 / 18 + 7 = 35.

# Distance Calculation

We need to solve the equation to find the values of d1 and d2.

Let's solve the equation:

d1 / 24 + d2 / 18 + 7 = 35

Multiplying through by the common denominator, we get:

18d1 + 24d2 + 7 * 24 * 18 = 35 * 24 * 18

Simplifying further, we have:

18d1 + 24d2 + 3024 = 15120

Rearranging the terms, we get:

18d1 + 24d2 = 12120

We have one equation with two variables, so we cannot find the exact values of d1 and d2. However, we can find the relationship between d1 and d2.

Let's solve the equation for d1 in terms of d2:

d1 = (12120 - 24d2) / 18

# Distance Traveled

To find the total distance traveled by the boat, we need to calculate the sum of d1 and d2.

Total distance = d1 + d2

Substituting the value of d1 in terms of d2, we get:

Total distance = (12120 - 24d2) / 18 + d2

Simplifying the equation, we have:

Total distance = (12120 - 24d2 + 18d2) / 18

Combining like terms, we get:

Total distance = (12120 - 6d2) / 18

Now, we can calculate the total distance traveled by the boat.

Answer

The total distance traveled by the boat can be calculated using the equation: Total distance = (12120 - 6d2) / 18.

Please note that we were unable to find the exact values of d1 and d2 due to the equation having two variables and one equation. However, we have derived the relationship between d1 and d2 and provided a formula to calculate the total distance traveled by the boat.