1950 AMC 12 Problem 19

Attempt Problem 19 of the 1950 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1950 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

19.

If mm men can do a job in dd days, then m+rm+r men can do the job in:
d+rd+r days
d−rd-r days
mdm+r\dfrac{md}{m+r} days
dm+r\dfrac{d}{m+r} days
None of these
Answer: C
Concepts:rateratio and proportion
Small hint:
Measure the total job in man-days
Big hint:
The original crew performs mdmd man-days of work
Solution:
The job requires m⋅d=mdm\cdot d=md man-days. With m+rm+r men working at the same individual rate, the required number of days is mdm+r. \frac{md}{m+r}.
Thus, the correct answer is C.
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