Math Problems, Proportions Problems

Problem of the Day: 2/28/13

A bathtub can fill to the top in 30 minutes. The drain can empty the tub in 45 minutes. If the tap is on and the drain open, how long will the bathtub take to fill?

Solution to yesterday’s problem:

Let’s list the factors of 60 to consider some of the possible integers.

1,60
2,30
3,20
4,15
5,12
6,10

We can say that two of the three integers must have a product of one of the factors because they are part of the product to make 60. We might reason that if the factors are closer together, then the sum will be smaller. So for (6,10), we can form (6,5,2) and (3,2,10) as two possible sets of factors. The sum of (6,5,2) is less: only 13. However, we’d better check some of the other factors because some of the larger numbers may have small factors as well. After a little trial and error, we find that (3,5,4) has a sum of 12. So the least possible sum of the factors is 12.

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