Question 1026386
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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?
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A small pipe's rate is  {{{1/8}}}  vat-volume-per-hour.

A large pipe's rate is  {{{1/6.5}}}  vat-volume-per-hour.

When both pipes work, their combined rate is 

{{{1/8 + 1/6.5}}} = {{{1/8 + 2/13}}} = {{{13/(8*13) + (2*8)/(8*13)}}} = {{{13/104 + 16/104}}} = {{{(13 + 16)/104}}} = {{{29/104}}}.

It means that two pipes working together fill  {{{29/104}}}  of the vat volume per hour.

Hence, they will fill the vat in  {{{104/29}}}  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
<A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using fractions to solve word problems on joint work</A>  in this site.

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