Tom, Dick and Harry piled stones into a pyramid to my precise specifications. Fred, an efficiency expert carefully watched them.
When the pyramid was complete, Fred reported that if Tom had worked twice as fast the job would have taken exactly 2 hours less, if Dick had worked three times as fast the job would have taken exactly 3 hours less, and if Harry had worked four times as fast the job would have taken exactly 4 hours less.
How long had the job taken?
For simplicity call the rates at which the men had worked A, B and C, measured in jobs per hour.
1/(A+B+C) = 1/(2*A+B+C)+2
1/(A+B+C) = 1/(A+3*B+C)+3
1/(A+B+C) = 1/(A+B+4*C)+4
Wolfram Alpha solves:
A˜0.043706 - 4.87627×10^-16 i
B˜0.0395547 - 1.40567×10^-15 i
C˜0.0443204 + 1.62376×10^-15 i
but we can ignore the imaginary components as rounding error, and the time taken would be
1/(0.043706 + 0.0395547 + 0.0443204)
or about 7.838 hours, or 7 hours, 50 minutes.
(The imaginary components shrink to tinier orders of magnitude as larger numbers of digits are asked for.)
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Posted by Charlie
on 2023-12-23 13:32:21 |
solution
