SOLUTION: A small pipe can fill a vat with water in 8 hours. A larger pipe can fill the same vat in only 6.5 hours. How long would it take to fill the vat if the two pipes are working at the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A small pipe can fill a vat with water in 8 hours. A larger pipe can fill the same vat in only 6.5 hours. How long would it take to fill the vat if the two pipes are working at the      Log On


   

Question 1026386: A small pipe can fill a vat with water in 8 hours. A larger pipe can fill the same vat in only 6.5 hours. How long would it take to fill the vat if the two pipes are working at the same time?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
A small pipe can fill a vat with water in 8 hours. A larger pipe can fill the same vat in only 6.5 hours.
How long would it take to fill the vat if the two pipes are working at the same time?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

A small pipe's rate is  1%2F8  vat-volume-per-hour.

A large pipe's rate is  1%2F6.5  vat-volume-per-hour.

When both pipes work, their combined rate is 

1%2F8+%2B+1%2F6.5 = 1%2F8+%2B+2%2F13 = 13%2F%288%2A13%29+%2B+%282%2A8%29%2F%288%2A13%29 = 13%2F104+%2B+16%2F104 = %2813+%2B+16%29%2F104 = 29%2F104.

It means that two pipes working together fill  29%2F104  of the vat volume per hour.

Hence, they will fill the vat in  104%2F29  hours.

Unfortunately, these numbers and this ratio are so curve, that the question arises: 
who invented this condition and for what purposes. Definitely, it was not me.

If you want to see more solved problems on joint work, look into the lesson
Using fractions to solve word problems on joint work  in this site.

They are really nice problems, and you really will benefit from reading it.