Question 184242
An inlet pipe can fill Dominica's pool in 7 hr, while an outlet pipe can empty
 it in 11 hours. In his haste to watch television, Dominica left both pipe open.
 How long did it take to fill the pool.
:
TV is a brain destroyer, avoid it at all costs!
:
Let t = time required when both pipes are open
:
Let the completed job = 1 (full pool)
:
Fill is +, emptying is -
:
{{{t/7}}} - {{{t/11}}} = 1
Multiply equation by 77:
77*{{{t/7}}} - 77*{{{t/11}}} = 77(1)
cancel out the denominators:
11t - 7t = 77
4t = 77
t = {{{77/4}}}
t = 19.25 hrs or 19 hrs 15 min
:
:
Check solution
{{{19.25/7}}} - {{{19.25/11}}} = 1
2.75 - 1.75 = 1, confirms our solution