SOLUTION: please help me solve this question... a pool has two pumps. Pump A empties the pool in 4 hours. Pump B empties the pool in 12 hours. How long will it take to empty the pool if both

Algebra ->  Rectangles -> SOLUTION: please help me solve this question... a pool has two pumps. Pump A empties the pool in 4 hours. Pump B empties the pool in 12 hours. How long will it take to empty the pool if both      Log On


   

Question 477221: please help me solve this question... a pool has two pumps. Pump A empties the pool in 4 hours. Pump B empties the pool in 12 hours. How long will it take to empty the pool if both pumps are working together? thanks so much

i think the answer is 3?...i divided 3 into 12..not sure if thats correct
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of pump A: 1/4 of a pool per hour


Rate of pump B: 1/12 of a pool per hour


Combined rate: 1/4+1/12 = 3/12+1/12 = 4/12 = 1/3


So if they work together, the two pumps have a combined rate of 1/3 of a pool per hour (ie in one hour, the two pumps will empty 1/3 of the pool)


But we want to empty ONE pool (not 1/3 of one). So we need to multiply 1/3 by some number x to get 1. So


%281%2F3%29x=1


Now solve for x


%281%2F3%29x=1


x=1%2A3


x=3


So it will take the two pumps 3 hours to empty the pool.