Question 600545
a swimming pool can be filled by pump A in 3 hrs and by pump B in 6 hrs, each pump working on its own.
 at 9AM. pump A is started. at what time will the swimming pool be filled if pump B is started at 10AM?
:
Let t = the pumping time of the B pump
then
(t+1) = the pumping time of the A
:
Let the completed job = 1 (a full pool)
:
Pump B + Pump A = a full pool
{{{t/6}}} + {{{((t+1))/3}}} = 1
Multiply by 6
6*{{{t/6}}} + 6*{{{((t+1))/3}}} = 6(1)
Cancel the denominators, results:
t + 2(t+1) = 6
t + 2t + 2 = 6
3t = 6 - 2
3t = 4
t = 4/3 hrs which is 1 hr 20 min, 
Full pool at 11:20 
:
:
See if that checks out
{{{1.33/6}}} + {{{2.33/3}}} = 
.2217 + .7767 = .998 ~ 1



Full pool at 12 PM