Expert: Sherry Wallin - 3/15/2009

Question
A pipe can fill up the tank with the drain pipe open in 3 hours. If the pipe runs with the drain open for one hour and then the drain is closed, it will take 45 more minutes for the pipe to fill up the tank. If the drain will be closed right at the start of filling, how long will the pipe be able to fill up the tank?


Answer
Lawrence~
    Hi. I hope you like fractions because these problems are best done with ratios. If a pipe can fill a tank in 3 hours with a drain open this means with the drain open the tank is being filled at a rate of 1 tank per 3 hours or 1/3 tank per hour. So there is 2/3 tank left to be filled which is being filled with the drain closed in 45 minutes = 3/4 hour. So the rate the tank gets filled with the drain closed is the ratio of 2/3 tank per 3/4 hour, so 2/3 divided by 3/4 is 8/9 of an hour. To find out how long it would take to fill the tank with the drain closed let x = the time and say (work = rate*time) 1 tank = (8/9)x
so x = 9/8 of an hour to fill the whole tank with the drain closed.

Hope this make sense. This is a rate problem and that is why ratios work so well and why we use fractions to solve it. The other important part is that this type of rate problem is a work problem. Typically work is equivalent to one job and if it takes x hours to do 1 job then you can do 1/x jobs per hour where 1/x is the rate. It is no surprise above that the answer is 9/8 since 9/8 is the reciprocal of 8/9 and we always examine work as being 1 job, i.e, (8/9)(9/8) = 1 job where 8/9 is the rate and 9/8 is the time.

Math Prof