Pumps A and B

[heshamelaziry]

Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will take to empty the pool?

OA[spoiler] A(B + 1)/ A + B[/spoiler]

[aspirant1]

rate pump A = 1/A
rate pump B = 1/B

Pump A worked for 1 minute alone, so work done = 1/A (amount of water emptied by pump A for 1 minute)

remaining water = 1-(1/A)

Both pumps working together = 1+ [(1- (1/A)) / ((1/A)+(1/B))] = A(1+B)/(A+B)

good one!

[ssuarezo]

rate pump A = 1/A
rate pump B = 1/B

Pump A worked for 1 minute alone, so work done = 1/A (amount of water emptied by pump A for 1 minute)

remaining water = 1-(1/A)

Both pumps working together = = A(1+B)/(A+B)

good one!

Hi Aspirant:

You have (remaining water/sum of rates) and you add 1 because of the minute already gone ! .. I didn't get it ... Thank you.

Silvia

Silvia.

[aspirant1]

yeah, pump A has already worked for 1 minute