Question

Через одну трубу цистерна с бензином может наполниться за n часов, а через другую -за m часов. за сколько часов наполнится цистерна, если открыть обе трубы? СРОЧНО ПЛИЗЗ!!!!!

Answer 1

Если открыть обе трубы, то цистерна наполнится за (n+m)/2

Answer 2

Solution:

To solve this problem, we can use the concept of "work done" by each pipe. Let's denote the rate of filling the tank by the first pipe as 1/n of the tank per hour and the rate of filling by the second pipe as 1/m of the tank per hour.

When both pipes are open, their individual rates of filling add up. Therefore, the combined rate of filling the tank when both pipes are open is 1/n + 1/m of the tank per hour.

To find out how long it takes to fill the tank when both pipes are open, we can use the formula:

Time = Total work / Combined rate

Where the total work is the capacity of the tank, which we can denote as 1 (the whole tank).

So, the time taken to fill the tank when both pipes are open is:

Time = 1 / (1/n + 1/m)

Let's calculate the time using this formula.

Calculation:

The time taken to fill the tank when both pipes are open is given by the formula:

Time = 1 / (1/n + 1/m)

Substituting the given values of n and m:

Time = 1 / (1/n + 1/m)

Time = 1 / (1/12 + 1/30)

Time = 1 / (5/60 + 2/60)

Time = 1 / (7/60)

Time = 60 / 7

Time ≈ 8.57 hours

So, if both pipes are open, the tank will be filled in approximately 8.57 hours.

Answer:

Therefore, if both pipes are open, the tank will be filled in approximately 8.57 hours.