If a man can complete a task in 5 days on his own but can finish it in 3 days with his son’s assistance, how long would it take for his son to complete the task independently?
Question
If a man can complete a task in 5 days on his own but can finish it in 3 days with his son’s assistance, how long would it take for his son to complete the task independently?
Solution
Step 1: Identify what the problem is asking for. In this case, we want to find out how long it would take for the son to complete the task independently.
Step 2: Identify what information we have. We know that the man can complete the task in 5 days on his own, and that together with his son, they can complete the task in 3 days.
Step 3: Use the concept of work rate, which is the reciprocal of the time it takes to complete a task. The man's work rate is 1/5 (task/day) and the combined work rate of the man and his son is 1/3 (task/day).
Step 4: Subtract the man's work rate from the combined work rate to find the son's work rate. So, 1/3 - 1/5 = 2/15 (task/day).
Step 5: To find out how long it would take for the son to complete the task independently, take the reciprocal of the son's work rate. So, 15/2 = 7.5 days.
Therefore, it would take the son 7.5 days to complete the task independently.
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