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Zorluk: KolayWork Rate and Combined Work

A specialized mapping drone, Model X, can complete an aerial survey of a solar farm in 2020 hours operating alone at a constant rate. A second drone, Model Y, can complete the exact same survey in 3030 hours operating alone at a constant rate. If both drones operate simultaneously at their respective constant rates, how many hours will it take them to complete the aerial survey together?

Cevap: 12 hours

Cevap

It will take 12 hours for both drones operating together to complete the survey.
Model X completes 120\frac{1}{20} of the job per hour and Model Y completes 130\frac{1}{30} of the job per hour. Combined, their rate is 120+130=560=112\frac{1}{20} + \frac{1}{30} = \frac{5}{60} = \frac{1}{12} of the job per hour. Taking the reciprocal yields a total time of 12 hours.

Adım Adım Çözüm

1
Calculate individual work rates
Model X rate = 120\frac{1}{20} job/hr, Model Y rate = 130\frac{1}{30} job/hr
Work rate is the reciprocal of the total time required to complete one full job.
2
Calculate the combined rate of work
Combined rate = 120+130=560=112\frac{1}{20} + \frac{1}{30} = \frac{5}{60} = \frac{1}{12} job/hr
When working simultaneously, individual rates add together.
3
Compute total time required for combined work
Total time = 11/12=12\frac{1}{1/12} = 12 hours
Time is equal to total work (1 job) divided by the combined work rate.

Anahtar Kavram

Combined Work Rate formula: Ratetotal=Rate1+Rate2\text{Rate}_{\text{total}} = \text{Rate}_1 + \text{Rate}_2, and Timetotal=1Ratetotal\text{Time}_{\text{total}} = \frac{1}{\text{Rate}_{\text{total}}}.
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Work Rate and Combined Work

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