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June 15, 2005
Typing to Finish Fast
Two typists get together to prepare a report. The more experienced typist by himself could finish the job in 2 hours. The less experienced typist by herself could do it in 3 hours.
How long will it take them to do the job together if they divide it so as to spend the least time possible?
MathGolf: Challenge 38
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The more experienced typist types 1.5 times faster than the less experienced typist does.
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The more experienced typist types 1.5 times faster than the less experienced typist. His share should be 1.5 times larger than that of the other typist if both are to stop at the same time. So, the first typist should take 3/5 of the report, and the second typist should take 2/5 of the report.
The first typist can do the whole job in 2 hours. So, 3/5 of the job can be carried out in 2 x 3/5 = 6/5 hours (1 hour 12 minutes).
Thus, the shortest time required for both typists to type the report is 1 hour 12 minutes.
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