# math

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If pump A and pump B work together, they can fill a pool in 4 hours. Pump A, working alone, takes 6 hours to fill the pool. How long would it take pump B, working alone, to fill the pool?

• math -

rate of pump A = 1/6
rate of pump B = 1/x
combined rate = 1/6 + 1/x
= (x+6)/(6x)

time at combined rate = 1/( (x+6)/6x )
= 6x/(x+6)

but 6x/(x+6) = 4
6x = 4x+ 24
2x = 24
x = 12

Pump B alone would take 12 hours

check:
combinedrate =1/12 + 1/6 = 3/13 = 1/4
time at combined rate = 1/(1/4)) = 4

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