SOLUTION: If two taps A and B are turned on together, they will fill a tank in 1 hour and 20 minutes. If tap A is turned on for 10 minutes and then tap B is turned on for 12 minutes, only 2/
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Question 808614: If two taps A and B are turned on together, they will fill a tank in 1 hour and 20 minutes. If tap A is turned on for 10 minutes and then tap B is turned on for 12 minutes, only 2/15 of the tank is filled. How long does each tap take to fill the tank alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If two taps A and B are turned on together, they will fill a tank in 1 hour and 20 minutes.
Change this to 80 minutes
Let the full tank = 1
The shared work equation
+ = 1
multiply by ab, resulting in
80b + 80a = ab
;
If tap A is turned on for 10 minutes and then tap B is turned on for 12 minutes, only 2/15 of the tank is filled.
+ =
multiply by 15ab, resulting in:
15b(10) + 15a(12) = 2ab
150b + 180a = 2ab
Simplify, divide by 2
75b + 90a = ab
ab = ab therefore
75b + 90a = 80b + 80a
90a - 80a = 80b - 75b
10a = 5b
divide by 5
2a = b
Use the 1st equation, replace b with 2a
+ = 1
multiply by 2a
2(80) + 80 = 2a
240 = 2a
a = 240/2
a = 120 min tap A alone
then
2(120) = 240 min tap B alone
:
:
Check this on a calc
+ =
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