Today Puzzle #695
Tom, Pat and Harry work in the post office sorting room. On an average day, if Tom is not working Pat and Harry can sort the mail together in 40 minutes. If Pat is not working, Tom and Harry can sort the mail in one hour. If Harry is not working, Tom and Pat can sort the mail in 30 minutes. How long will it take all three of them, working together, to sort the mail on an average day?
Today’s #PuzzleForToday has been set by Dr Steve Humble MBE, Head of Education, Newcastle University
Click here for the answer
Working together it will take Tom, Pat and Harry 26.7 minutes to sort the mail.
Details of a possible solution.
Solving the following three equations gives us one way of obtaining the solution to this puzzle
(1/P) + (1/H) = (1/40)
(1/T) + (1/H) = (1/60)
(1/T) + (1/P) = (1/30)
Subtracting equation (2) from (1) gives (1/P) – (1/T) = (1/120)
Adding this result to equation (3): 2(1/P) = (1/20) and so P = 48 minutes.
With P= 48 in equation (1) give H = 240 and similarly we can find T = 80
The time (T) for all three, Tom, Pat and Harry, working together can be calculated from the equation (T/80) + (T/48) + (T/240) = 1 as 26.7 minutes
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