Question 181561
Pipes A and B can fill a storage tank in 8 hours and 12 hours, respectively. With the tank empty, pipe A was turned on at noon , and then pipe B was turned on at 1:30 pm. At what time was the tank full?
:
Let t = the "on" time duration of pipe A
then
(t-1.5) = the "on" time of pipe B
:
Let the completed job = 1; (a full tank)
:
A shared work equation:
{{{t/8}}} + {{{((t-1.5))/12}}} = 1
Multiply equation by 24 to get rid of the denominators, results:
3t + 2(t-1.5) = 24(1)
;
3t + 2t - 3 = 24
:
5t = 24 + 3
t = {{{27/5}}}
t = 5.4 hrs, which is 5 hrs + (.4*60) = 5 hrs, 24 min
:
we can say the tank will be full at 5:24 pm
;
:
Check solution; pipe B time: 5.4 - 1.5 = 3.9 hrs
{{{5.4/8}}} + {{{3.9/12}}} = 
.625 + .325 = 1; confirms our solution