Calculating Joint Work Time for Hotel Cleaning
This problem involves calculating the time it takes for two individuals, Sita and Rita, to complete a task (cleaning a hotel) when working together. We determine their individual rates of work and then combine these rates to find their joint rate.
Sita's Work Rate
Sita can clean the hotel in 20 days. Her work rate is the fraction of the hotel she cleans per day.
Sita's rate = $\frac{1}{\text{Days Sita takes}} = \frac{1}{20}$ hotel per day.
Rita's Work Rate
Rita can clean the same hotel in 30 days. Her work rate is:
Rita's rate = $\frac{1}{\text{Days Rita takes}} = \frac{1}{30}$ hotel per day.
Combined Work Rate
To find how fast they work together, we add their individual rates.
Combined rate = Sita's rate + Rita's rate
Combined rate = $\frac{1}{20} + \frac{1}{30}$
To add these fractions, we find a common denominator, which is 60.
Combined rate = $\frac{3}{60} + \frac{2}{60} = \frac{3+2}{60} = \frac{5}{60}$
Simplifying the combined rate:
Combined rate = $\frac{1}{12}$ hotel per day.
Time Taken Together
The time taken to complete the job together is the reciprocal of their combined rate.
Time together = $\frac{1}{\text{Combined rate}}$
Time together = $\frac{1}{\frac{1}{12}} = 12$ days.
Conclusion
Working together, Sita and Rita will take 12 days to clean the hotel.
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