Question

Расстояние между двумя городами почтовый голубь пролетает при отсутствии ветра за t = 60 мин., а при встречном ветре за время t2 = 75 мин. За какое время t1 голубь преодолеет это расстояние при попутном ветре? Решите, пожалуйста!

Answer 1

За 45 минут, так, как 60-15=45

Answer 2

Calculation of Time for the Pigeon to Cover the Distance

To determine the time it takes for the pigeon to cover the distance with a tailwind, we can use the concept of relative speed. The relative speed is the difference between the speed of the pigeon and the speed of the wind.

Let's assume the distance between the two cities is d.

Given: - Time taken by the pigeon to cover the distance without wind (tailwind) = t = 60 minutes. - Time taken by the pigeon to cover the distance with a headwind = t2 = 75 minutes.

To find: - Time taken by the pigeon to cover the distance with a tailwind = t1.

We can set up the following equation using the concept of relative speed:

d / (pigeon's speed + wind speed) = t

Since we are looking for the time taken with a tailwind, we need to consider the speed of the pigeon relative to the wind. Let's assume the speed of the pigeon is p and the speed of the wind is w.

For the headwind scenario: d / (p - w) = t2

For the tailwind scenario: d / (p + w) = t1

To find t1, we need to solve for d in terms of p and w using the given information.

Solution

To solve for d, we can set up a proportion using the two equations:

(d / (p - w)) / (d / (p + w)) = t2 / t1

Simplifying the equation:

(p + w) / (p - w) = t2 / t1

Cross-multiplying:

(p + w) * t1 = (p - w) * t2

Expanding:

p * t1 + w * t1 = p * t2 - w * t2

Rearranging the equation to solve for t1:

p * t1 - p * t2 = -w * t2 - w * t1

Factoring out t1:

t1 * (p - t2) = -w * (t2 + t1)

Dividing both sides by (p - t2):

t1 = -w * (t2 + t1) / (p - t2)

Now we can substitute the given values to find t1.

Calculation

Given: - t = 60 minutes - t2 = 75 minutes

We need to find t1.

Let's assume the speed of the pigeon is p and the speed of the wind is w.

Substituting the given values into the equation:

t1 = -w * (t2 + t1) / (p - t2)

Simplifying the equation:

t1 * (p - t2) = -w * (t2 + t1)

Expanding:

p * t1 - t2 * t1 = -w * t2 - w * t1

Rearranging the equation to solve for t1:

t1 * (p + w) = -t2 * (p + w)

Dividing both sides by (p + w):

t1 = -t2 * (p + w) / (p + w)

Simplifying further:

t1 = -t2

Since the wind speed is not given, we can conclude that the time taken by the pigeon to cover the distance with a tailwind is equal to the time taken with a headwind.

Therefore, t1 = t2 = 75 minutes.

So, the pigeon will take 75 minutes to cover the distance with a tailwind.

Please note that the given information does not provide enough details to determine the exact values of p and w. The solution is based on the assumption that the wind speed is not given and the time taken with a tailwind is equal to the time taken with a headwind.

I hope this helps! Let me know if you have any further questions.