Mathematical and Physical Journal
for High Schools
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Problem K. 362. (January 2013)

K. 362. Peter takes 5 hours to do a certain job alone, and Paul takes 6 hours to do the same job alone. When they work together, they are both behindered by their continual quarrelling about everything, and their productivity decreases: each of them will do the work at a rate lowered by the same percentage. By what percentage is it lowered if the two of them take 3.5 hours to finish the job together?

(6 pont)

Deadline expired on February 11, 2013.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Péter 1 óra alatt a munka 1/5, Pál pedig az 1/6 részét végzi el. Ha nem akadályoznák egymást, akkor 1 óra alatt a munka 1/5+1/6=11/30 részét végeznék el, ami 3,5 óra alatt a munka 38,5/30 része lenne. Valójában 3,5 óra alatt a munka 30/30 részét végzik el, így munkatempójuk az eredetinek a 30/38,5 része. Mivel 30/38,5=0,7792, így munkatempójuk 100-77,92=22,08%-kal romlik.


155 students sent a solution.
6 points:63 students.
5 points:15 students.
4 points:11 students.
3 points:36 students.
2 points:4 students.
1 point:7 students.
0 point:10 students.
Unfair, not evaluated:9 solutions.

Problems in Mathematics of KöMaL, January 2013