Question 741919
 two pipes p and q can fill a tank 12 and 15 minutes respectfully.
 if both are opened together, and at the end 3 minutes, the first is closed.
 how much longer will the tank take to fill?
:
Let t = additional time required to fill the tank
let the completed job = 1; (a full tank)
:
A shared work equation
:
{{{3/12}}} + {{{((t+3))/15}}} = 1
multiply by 60 to clear the denominators
60*{{{3/12}}} + 60*{{{((t+3))/15}}} = 60*1
cancel the denominators and you have
5(3) + 4(t+3) = 60
15 + 4t + 12 = 60
4t = 60 - 27
4t = 33
t = 33/4
t = 8.25 additional minutes
:
:
See if this check out (the 2nd pipe runs a total of 11.25 min)
{{{3/12}}} + {{{11.25/15}}} = 
.25 + .75 = 1; confirms our solution of t=8.25