Word Problems/Unit Rate
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: "4 pipes drain a tank in 70 minutes"
Each pipe drains ¼ of the tank in 70 minutes.
The rate is ¼ pipe/(70 minutes), but you want the numerator to be 1, so multiply the rate by 4/4:
(¼ pipe) / (70 minutes) × 4/4 = 1 pipe/(280 minutes)
It takes one pipe 280 minutes (or 4 hours and 40 minutes) to drain the tank.
---------- FOLLOW-UP ----------
I want to thank you for your reply.
What is wrong with my solution? I determined that it takes one pipe 280 minutes to drain the tank. Why is it necessary to determine 1/4 pipe per 70 minutes and then determine 1 pipe per 280 minutes from 1/4 pipe per 70 minutes?
To tell the truth, I am not sure how you came up with your expression, so I just went ahead and used the first solution that came to mind.
As is so often the case, there is more than one way to get there.
Here is another approach.
"4 pipes drain a tank in 70 minutes"
1 tank / (4 pipes × 70 minutes) = 1 tank / (280 pipe-minutes) = 1 tank / (1 pipe × 280 minutes)