Advanced Math/Unit Rate

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Question
Hello:

Have I determined the unit rate for the following correctly?

If 4 pipes can drain a tank in 70 minutes, how long will it take 1 pipe to drain the same tank?

Since 1 pipe will take longer than 4 pipes, is the following solution correct?

(4/1) X 70 minutes/(1/4) X 4 pipes will equal 280 minutes/1 pipe.

I think that the quantities are inversely proportional to each other.
The inverse of 4 is 1/4.

Usually to find the unit rate, divide the numerator and denominator by the denominator. In this situation, this method will not produce the correct answer because of the inverse relationship.

I thank you for your reply.

Answer
Hi Kenneth,
Yes, the inverse relationship means that you can't divide in that sense. In this case, the number of pipes multiplied by the time it takes to drain the tank is a constant, assuming pipes of equal characteristics. That information is enough to solve the problem, and so if it takes T minutes for one pipe to drain the same tank then;
4 pipes x 70 minutes = 1 pipe x T minutes
T = 280

Regards

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