Question

Теплоход проходит 40 1/2 км по течению реки за 1 1/2 ч. На сколько больше времени уйдет на обратный путь, если скорость течения равна 3 3/8 км/ч?

Answer 1

Problem Analysis

We are given that a boat travels 40 1/2 km upstream in 1 1/2 hours. We need to find out how much longer it will take for the boat to travel the same distance downstream, given that the speed of the current is 3 3/8 km/h.

Solution

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

Let's calculate the time it takes for the boat to travel upstream first.

The distance traveled upstream is 40 1/2 km, and the speed of the boat relative to the water is the difference between the boat's speed and the speed of the current. So the speed of the boat relative to the water is:

boat's speed relative to water = boat's speed - speed of current

We are not given the speed of the boat, so we cannot calculate the exact time it takes to travel upstream. However, we can still calculate the time difference for the return trip.

Let's assume the speed of the boat relative to the water is x km/h. Then the speed of the boat downstream is:

boat's speed downstream = boat's speed relative to water + speed of current

The time it takes to travel downstream is:

time downstream = distance / boat's speed downstream

To find the time difference, we need to subtract the time it takes to travel upstream from the time it takes to travel downstream:

time difference = time downstream - time upstream

Let's calculate the time difference.

Calculation

Given: - Distance traveled upstream = 40 1/2 km - Speed of current = 3 3/8 km/h

To calculate the time difference, we need to find the time it takes to travel downstream and upstream.

First, let's calculate the time it takes to travel upstream.

We are not given the speed of the boat, so we cannot calculate the exact time it takes to travel upstream. However, we can still calculate the time difference for the return trip.

Let's assume the speed of the boat relative to the water is x km/h. Then the speed of the boat downstream is:

boat's speed downstream = x + 3 3/8 km/h

The time it takes to travel downstream is:

time downstream = distance / boat's speed downstream

Substituting the given values, we have:

time downstream = 40 1/2 km / (x + 3 3/8 km/h)

Now, let's calculate the time it takes to travel upstream.

The speed of the boat relative to the water is:

boat's speed relative to water = x - 3 3/8 km/h

The time it takes to travel upstream is:

time upstream = distance / boat's speed relative to water

Substituting the given values, we have:

time upstream = 40 1/2 km / (x - 3 3/8 km/h)

Finally, let's calculate the time difference:

time difference = time downstream - time upstream

Substituting the calculated values, we have:

time difference = (40 1/2 km / (x + 3 3/8 km/h)) - (40 1/2 km / (x - 3 3/8 km/h))

To find the exact time difference, we need to solve this equation. However, without the exact value of the boat's speed, we cannot calculate the exact time difference.

Therefore, the answer to the question "On how much longer will it take for the boat to travel the same distance downstream, given that the speed of the current is 3 3/8 km/h?" cannot be determined without knowing the speed of the boat.

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