Samuel can do a piece of work in 12 days and Bruce can do it in 6 days. If Carl, who can do the work in 16 days, joins them, then how long will they take to together complete the work? Ops: A. 7/8 days B. 16/5 days C. 24/5 days D. 13/25 days
Question
Samuel can do a piece of work in 12 days and Bruce can do it in 6 days. If Carl, who can do the work in 16 days, joins them, then how long will they take to together complete the work? Ops: A. 7/8 days B. 16/5 days C. 24/5 days D. 13/25 days
Solution
To solve this problem, we first need to find out how much work each person can do in one day.
- Samuel can do the work in 12 days, so in one day, he can do 1/12 of the work.
- Bruce can do the work in 6 days, so in one day, he can do 1/6 of the work.
- Carl can do the work in 16 days, so in one day, he can do 1/16 of the work.
If they all work together in one day, they can do (1/12 + 1/6 + 1/16) of the work.
To simplify this, we need to find a common denominator. The least common multiple of 12, 6, and 16 is 48.
So, (1/12 + 1/6 + 1/16) becomes (4/48 + 8/48 + 3/48) = 15/48 of the work in one day.
Therefore, to complete the whole work, they will take 48/15 days.
When we simplify 48/15, we get 16/5 days.
So, the answer is B. 16/5 days.
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