Question

Между городами A и B, расположенными на реке, курсирует лодка, которая, двигаясь по течению, проходит расстояние между A и B за 3 часа, а против течения — за 9 часов. За сколько часов лодка доберётся из A в B и обратно, если увеличит скорость относительно воды вдвое? Ответ округлите до десятых. ПЛИЗ . ДАМ 100 БАЛОВ...

Answer 1

Ответ:на фото:)

Объяснение:

Answer 2

Problem Analysis

To solve this problem, we need to calculate the time it takes for a boat to travel from point A to point B and back, given that it takes 3 hours to travel from A to B with the current and 9 hours to travel from B to A against the current. Additionally, the boat's speed relative to the water will be doubled.

Solution

Let's denote the speed of the boat as V and the speed of the current as C. The boat's speed relative to the water when moving with the current is V + C, and when moving against the current, it's V - C.

We can use the formula: Time = Distance / Speed

When moving with the current: - Time = Distance / (V + C) - Distance = 3(V + C) (as it takes 3 hours to travel from A to B)

When moving against the current: - Time = Distance / (V - C) - Distance = 9(V - C) (as it takes 9 hours to travel from B to A)

We need to solve for V and C, and then calculate the time for the round trip.

Calculation

Let's solve for V and C using the given information: 1. 3(V + C) = Distance 2. 9(V - C) = Distance

We'll then double the boat's speed relative to the water and calculate the time for the round trip.

Solution Steps

1. Solve for V and C using the given information. 2. Double the boat's speed relative to the water. 3. Calculate the time for the round trip.

Solution

1. Solving for V and C: - From the given information, we have: - 3(V + C) = Distance - 9(V - C) = Distance - Solving the above equations simultaneously: - 3V + 3C = Distance - 9V - 9C = Distance

- Adding the two equations: - 3V + 3C + 9V - 9C = 12V - 12V - 6C = 12V - 6C = 0 - C = 0

- Substituting C = 0 into equation 1: - 3V + 3(0) = Distance - 3V = Distance - V = Distance / 3

- Therefore, the boat's speed relative to the water when moving with the current is V = Distance / 3.

2. Doubling the boat's speed relative to the water: - The new speed of the boat relative to the water when moving with the current is 2V = 2(Distance / 3) = 2/3 * Distance.

3. Calculating the time for the round trip: - When moving with the current, the time taken is Distance / (2/3 * Distance) = 3/2 hours. - When moving against the current, the time taken is Distance / (1/3 * Distance) = 3 hours.

Conclusion

The boat will take 3/2 hours to travel from A to B and back, if its speed relative to the water is doubled.