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?
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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
{{{16/x}}} + {{{16/(2x)}}} = 1
Multiply eq by 2x and you have:
2(16) + 16 = 2x
:
32 + 16 = 2x
x = {{{48/2}}}
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
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This is good simple method to handle these "shared work problems".