Jack alone can complete a work in 12 days and Jill alone can complete the same work in 24 days. In how many days can Jack and Jill together complete the same work?6 days4 days10 days8 days
Question
Jack alone can complete a work in 12 days and Jill alone can complete the same work in 24 days. In how many days can Jack and Jill together complete the same work?6 days4 days10 days8 days
Solution
To solve this problem, we first need to find out how much work Jack and Jill can do in one day.
- Jack can complete the work in 12 days, so in one day, he completes 1/12 of the work.
- Jill can complete the work in 24 days, so in one day, she completes 1/24 of the work.
When Jack and Jill work together, their one day's work will be the sum of their individual one day's work.
So, Jack and Jill together can do (1/12 + 1/24) of the work in one day.
To simplify this, find a common denominator for 12 and 24, which is 24.
So, (2/24 + 1/24) = 3/24 = 1/8 of the work in one day.
Therefore, Jack and Jill together can complete the work in 8 days.
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