SOLUTION: A and B are two taps require to fill one tank in 15 hour.these two taps are kept open for 12 hours then tap B is closed then tank required more 8 hours to fill then find the time t

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Question 1098982: A and B are two taps require to fill one tank in 15 hour.these two taps are kept open for 12 hours then tap B is closed then tank required more 8 hours to fill then find the time that tap require to fill the tank seperately
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Ba%5D+ = the rate of filling of A tap
in [ tanks ] / [ hr ]
Let +R%5Bb%5D+ = the rate of filling of B tap
in [ tanks] / [ hr ]
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(1) +R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F15+
+12%2F15+=+4%2F5+ of the tank is filled in 12 hrs
with both taps open. +1%2F5+ of the tank is
left to be filled. Tap B is closed
(2) +R%5Ba%5D+=+%28+1%2F5+%29%2F8+
-----------------------------------------
(2) +R%7Ba%7D+=+1%2F40+
and
(1) +1%2F40+%2B+R%5Bb%5D+=+1%2F15+
multiply both sides by +15%2A40+
(1) +15+%2B+600R%5Bb%5D+=+40+
(1) +600R%5Bb%5D+=+25+
(1) +R%5Bb%5D+=+1%2F24+
-----------------------
Tap A takes 40 hrs to fill tank by itself
Tap B takes 24 hrs to fill tank by itself
-----------------------------------
check:
(1) +R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F15+
(1) +1%2F40+%2B+1%2F24+=+1%2F15+
Multiply both sides by +40%2A15+
(1) +15+%2B+25+=+40+
(1) +40+=+40+
OK