SOLUTION: Pipes A and B can fill a storage tank in 8 hours and 12 hours, respectivley. With the tank empty, pipe A was turned on at noon , and then pipe B was turned on at 1:30 pm. At what

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Question 181561This question is from textbook Algebra and Trigonometry Structure and Method
: Pipes A and B can fill a storage tank in 8 hours and 12 hours, respectivley. 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 ws the tank full? This question is from textbook Algebra and Trigonometry Structure and Method

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F8 + %28%28t-1.5%29%29%2F12 = 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%2F5
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%2F8 + 3.9%2F12 =
.625 + .325 = 1; confirms our solution