SOLUTION: One pump can fill a tank twice as fast as the second pump. If the pumps are used together, they will fill the tank in 16 minutes. How long would it take each pump working alone t

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Question 185240: One pump can fill a tank twice as fast as the second pump. If the pumps are used together, they will fill the tank in 16 minutes. How long would it take each pump working alone to fill the tank?
I can get what I believe is the right answer but don't know the rule because I really ended up with trial and error approach.
I used X for the one (slow)pump and 2X as the second (fast) pump and know they equal 16 minutes - so 3X = 16. Then I inverted to get 1/3x=16 or X=48 and then the fast pump would be 24 (1/2X). So the answer I get is that the fast pump by itself would take 24 minutes and the slow pump by itself would take 48 minutes. When I do a check and add 1/24 + 1/48 = 2/48 + 1/48 = 3/48 = 1/16 and then reinvert I get 16. This seems more trial and error than buy using a repeatable formula. Thanks for helping!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
One pump can fill a tank twice as fast as the second pump. If the pumps are used together, they will fill the tank in 16 minutes. How long would it take each pump working alone to fill the tank?
;
We can do this much simpler:
Like you did;
x = time of the fast pump to fill the tank
and
2x = time of the slow pump to do it
:
Let the completed job (full tank) = 1
:
A working together equation, each doing a fraction, which will add up to 1
+ = 1
Multiply eq by 2x and you have:
2(16) + 16 = 2x
:
32 + 16 = 2x
x =
x = 24 min the fast pump alone
and
48 min the slow pump alone
:
:
check solution:
16/24 + 16/48
2/3 + 1/3 = 1
;
This is good simple method to handle these "shared work problems".