Question 324846
autumn has come and you need to empty your swimming pool at home. you have an older water pump that can empty your swimming pool in 5 hours. you also just bought a new water pump since it was on sale and it can empty your swimming pool in 3 hours. you want to get the pool drained as quickly as possible so you can go out for a run. you decide to use both water pumps to empty your swimming pool at once. how long will it take the pool using both water pumps? 
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Older pump DATA:
time = 5 hrs/job ; rate = 1/5 job/hr
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Newer pump DATA:
time = 3 hrs/job ; rate = 1/3 job/hr
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Together DATA:
time = x hrs/job ; rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/5 + 1/3 = 1/x
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Multiply thru by 15x to get:
3x + 5x = 15
8x = 15
x = 15/8 hrs (time required for both pumpts to empty the pool together)
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Cheers,
Stan H.