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Word Problems/Indirect Proportion

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Question
Hello:

4 pipes can fill a tank in 70 minutes; how long will it take to fill the tank by 7 pipes?
Answer: 40 minutes

Is it possible to determine the answer with some calculation by using 70 minutes/4 pipes and by using 4 pipes/70 minutes?

I thank you for your reply.

Answer
They shouldn't be divided.

A pipe is putting in X amount of fluid per minute, or X/min, then multiplying by the number of minutes, say T, would give us TX for the total amount of fluid.  This amount will be some constant, as is TX = K.  If we must n pipes, then we have nTX = K.  This makes sense in that if we double the number if pipes n, it would give us half the time.

Now to apply it what we have.  It is known that the number of pipes times the time involved is a constant.  If it takes 4 pipes a total of 70 minutes, just take 4*70 and get 280 as the constant involved.

This means if we only had one pipe, it would take 280 minutes.

If we had two pipes, it would take 280/2 = 140 minutes.  This makes sense in that if we double the number of pipes it only takes half as one.

If we double again, and have 4 pipes, it would take 280/4 = 70 minutes, which is what was given.

If we had five pipes, it would take 280/5 = 56 minutes.

If we had 7 pipes, it would take 280/7 = 40 minutes.


What is necessary in this problem is found in physics, in that the units used must always cancel.  The exact quantities were not known, but a constant was found.  We don't know that number of gallons, but the input from a pipe is in X gallons/minute and time is in minutes,
so multiplying gives us gallons * minutes / gallons = minutes.

Hopefully you now have an understanding of how to get the minutes.

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