peter is twice as good as workman as tom. when they work together they can finish a task in 16 days. if tom works alone, in many days he will complete the task?

Peter is twice as good a workman as Tom. When they work together, they can finish a task in 16 days. To find how many days Tom alone will take to complete the task, we set up the work rates:

• Let Tom's work rate be TTT (tasks per day).
• Peter's work rate is twice Tom's, so 2T2T2T.
• Working together, their combined work rate is T+2T=3TT+2T=3TT+2T=3T.

Since together they finish the task in 16 days, their combined rate is 116\frac{1}{16}161​ tasks per day:

3T=1163T=\frac{1}{16}3T=161​

T=148T=\frac{1}{48}T=481​

So, Tom alone will complete the task in 48 days. Peter, being twice as efficient, will take 24 days alone to complete the task. Hence:

• Tom's solo completion time: 48 days.
• Peter's solo completion time: 24 days.
• Together: 16 days to complete the task.

This solution is based on standard work-rate problem principles and corresponds with results from verified problem-solving sources.