Peter can do a piece of work in 8 days Sam in 10 days and John in 16 days Sam and John work together for 4 days and then John is replaced by Peter find when the work will be finished.
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Answer:
step by step soln
Step-by-step explanation:
Let's assume that the total work to be done is represented by W.
We know that Peter can finish the work in 8 days, so his daily work rate is W/8.
Similarly, Sam can finish the work in 10 days, so his daily work rate is W/10.
And John can finish the work in 16 days, so his daily work rate is W/16.
When Sam and John work together for 4 days, their combined work rate is (W/10) + (W/16) = (8W + 5W)/(80) = (13W/80) per day.
So, in the 4 days, their total work done is (13W/80) x 4 = (13W/20).
Now, John is replaced by Peter. Let's assume that Peter works for x more days to finish the work.
In these x days, Sam and Peter will work together to complete the remaining work. So, their combined work rate is (W/10) + (W/8) = (9W/40) per day.
Thus, in x days, the total work done by Sam and Peter together will be (9W/40) x x = (9Wx/40).
As we know that the total work is equal to the sum of the work done by Sam and John in the first 4 days and the work done by Sam and Peter in the next x days. Therefore, we can write:
(13W/20) + (9Wx/40) = W
Simplifying this equation, we get:
26W + 9Wx = 40W
9Wx = 14W
x = (14/9) days
Therefore, Peter will work for an additional (14/9) days to complete the remaining work.