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Zorluk: OrtaWork Rate and Combined Work

An oceanographic research station uses two deep-sea water sampling pumps, Pump AA and Pump BB, to fill a designated storage tank with seawater. Working alone at its constant rate, Pump AA can fill the tank in 1010 hours. Working alone at its constant rate, Pump BB can fill the tank in 1515 hours. If Pump AA begins filling the empty tank alone and operates for 44 hours before shutting down, after which Pump BB operates alone to finish filling the tank, how many total hours does it take to fill the tank?

Cevap: 13 hours

Cevap

The total time required to fill the storage tank is 13 hours.
Pump A completes 2/5 of the tank during its 4 hours of operation. The remaining 3/5 of the tank is filled by Pump B in 9 hours. Summing the 4 hours from Pump A and the 9 hours from Pump B gives a total time of 13 hours.

Adım Adım Çözüm

1
Calculate individual work rates
Pump A rate = 1/10 tank/hour; Pump B rate = 1/15 tank/hour
Work rate is equal to the fraction of the job completed per unit of time (1 divided by total time).
2
Calculate work completed during the first stage
Work done by Pump A = 4 * (1/10) = 2/5 of the tank
Work completed equals work rate multiplied by operating time.
3
Determine the remaining work
Remaining work = 1 - 2/5 = 3/5 of the tank
The entire job is represented by 1 whole unit.
4
Calculate time required for the second stage
Time for Pump B = (3/5) / (1/15) = 9 hours
Time taken equals remaining work divided by the rate of Pump B.
5
Sum the time for both stages
Total time = 4 + 9 = 13 hours
The question asks for the total elapsed time from the start of filling to completion.

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Work Rate and Combined Work
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Work Rate and Combined Work

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