Question

Против течения паром двигается со скоростью y км/ч, а по течению в два раза быстрее. Запишите на математическом языке:A) по течению за 3 часа паром прошёл 12кмБ)по течению за 2 часа паром прошёл расстояние на 2 км большее, чем за 3 часа , двигаясь против течения

Answer 1

Против течения - у км/ч
По течению - 2у км/ч
а) 2у х 3=12 (км)
б) 12-3у=2 (км)

Answer 2

Problem Analysis

We are given that a ferry is moving against the current with a speed of "y" km/h, and with the current, it moves twice as fast. We need to express the given information mathematically and solve for the distance traveled in two different scenarios.

Mathematical Representation

Let's represent the speed of the ferry in still water as "x" km/h. Since the ferry moves twice as fast with the current, its speed with the current will be "2x" km/h. Similarly, since the ferry moves against the current, its speed against the current will be "x - y" km/h.

Scenario A: Distance Traveled in 3 Hours

In this scenario, the ferry is moving with the current. We are given that the ferry traveled a distance of 12 km in 3 hours. We can use the formula "distance = speed × time" to represent this scenario mathematically.

The distance traveled with the current can be calculated as: distance = speed × time 12 = (2x) × 3 12 = 6x x = 2

Therefore, the speed of the ferry in still water is 2 km/h.

Scenario B: Distance Traveled in 2 Hours

In this scenario, the ferry is moving against the current. We are given that the ferry traveled a distance that is 2 km greater than the distance traveled in 3 hours. We can use the formula "distance = speed × time" to represent this scenario mathematically.

The distance traveled against the current can be calculated as: distance = speed × time distance = (x - y) × 2 distance = (2 - y) × 2

We are also given that this distance is 2 km greater than the distance traveled in 3 hours. Mathematically, we can represent this as: (2 - y) × 2 = 12 + 2 4 - 2y = 14 -2y = 10 y = -5

However, since speed cannot be negative, this solution is not valid. Therefore, there is no valid solution for this scenario.

Summary

- In scenario A, where the ferry is moving with the current, the speed of the ferry in still water is 2 km/h. - In scenario B, where the ferry is moving against the current, there is no valid solution for the given information.

Please let me know if I can help you with anything else.