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23 Sep 2023, 05:16
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D
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Alice can complete a specific task in 20 days. She starts the task and works on it for 4 days, after which Bob takes over and finishes the remaining work in an additional 4 days. How long will it take for Alice and Bob to complete the task if they work together?
A. 2 days
B. 2.5 days
C. 3 days
D. 4 days
E. 5 days
A. 2 days
B. 2.5 days
C. 3 days
D. 4 days
E. 5 days
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23 Sep 2023, 06:44
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Bunuel
Let's assume Alice does 1 unit of work each day. Rate of Alice = 1 unit/day
Total work = \(20 * 1 = 20\) units
In the first 4 days, Alice does \(1 * 4 = 4\) units of work.
Remaining work = \(20 - 4 = 16\) units.
Bob takes over and completes the work in 4 days. Rate of Bob = \(\frac{16}{4} = 4\) units / day
If Alice and Bob work together, the amount of work done / day = 1 unit + 4 units = 5 units/day.
Number of days required = \(\frac{20}{5} = 4\) days
Option D
20 Mar 2024, 10:09
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Official Solution:
Alice can complete a specific task in 20 days. She starts the task and works on it for 4 days, after which Bob takes over and finishes the remaining work in an additional 4 days. How long will it take for Alice and Bob to complete the task if they work together?
A. 2 days
B. 2.5 days
C. 3 days
D. 4 days
E. 5 days
Since Alice completes the task in 20 days, in 4 days she completes 1/5 of the task, leaving 4/5 of the task to be completed by Bob. Since Bob finishes 4/5 of the task in 4 days, his rate is (job)/(time) \(= \frac{( \frac{4}{5})}{4} = \frac{1}{5}\) task per day. Hence, their combined rate is \(\frac{1}{20} + \frac{1}{5} = \frac{1}{4}\) task per day, which means that together they would take 4 days to complete the task.
Alternatively, we can assume Alice does 1 unit of the task per day, making the entire task equal to 20 units. In 4 days, she would complete 4 units of the task, leaving 16 units to be finished by Bob in 4 days. Thus, Bob completes 4 units of the task per day. Together, Alice and Bob do \(1 + 4 = 5\) units of work per day, which means that 20 units would take them \(\frac{20}{5} = 4\) days to complete.
Answer: D
Alice can complete a specific task in 20 days. She starts the task and works on it for 4 days, after which Bob takes over and finishes the remaining work in an additional 4 days. How long will it take for Alice and Bob to complete the task if they work together?
A. 2 days
B. 2.5 days
C. 3 days
D. 4 days
E. 5 days
Since Alice completes the task in 20 days, in 4 days she completes 1/5 of the task, leaving 4/5 of the task to be completed by Bob. Since Bob finishes 4/5 of the task in 4 days, his rate is (job)/(time) \(= \frac{( \frac{4}{5})}{4} = \frac{1}{5}\) task per day. Hence, their combined rate is \(\frac{1}{20} + \frac{1}{5} = \frac{1}{4}\) task per day, which means that together they would take 4 days to complete the task.
Alternatively, we can assume Alice does 1 unit of the task per day, making the entire task equal to 20 units. In 4 days, she would complete 4 units of the task, leaving 16 units to be finished by Bob in 4 days. Thus, Bob completes 4 units of the task per day. Together, Alice and Bob do \(1 + 4 = 5\) units of work per day, which means that 20 units would take them \(\frac{20}{5} = 4\) days to complete.
Answer: D
