Problem K. 592. (September 2018)

K. 592. Ann, Belle and Charlotte are doing a job together. The three of them finish it 6 hours sooner than Ann would finish it alone, 1 hour sooner than Belle would finish it alone, and they take half as much time together as Charlotte would take alone. If Ann and Belle work together without Charlotte, they finish the job in 80 minutes. How long would it take each girl Ann and Belle to do the job alone? (Express your answer in minutes.)

(6 pont)

Deadline expired on October 10, 2018.

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

Megoldás. Cili a saját idejének fele alatt a fele munkát végzi el, tehát Anna és Bea együttesen ennyi idő alatt szintén a fele munkát végzik el. Anna és Bea a fele munkát \(\displaystyle 40\) perc alatt végzik el, mert nekik \(\displaystyle 80\) percig tart az egész. Így a három lány együtt \(\displaystyle 40\) perc alatt végez. Tehát Anna egyedül \(\displaystyle 40+6\cdot60=400\) perc alatt, Bea egyedül \(\displaystyle 40+60=100\) perc alatt végezne a munkával.

Statistics:

137 students sent a solution.
6 points:	85 students.
5 points:	11 students.
4 points:	3 students.
3 points:	1 student.
2 points:	2 students.
1 point:	6 students.
0 point:	14 students.
Unfair, not evaluated:	1 solutions.
Not shown because of missing birth date or parental permission:	14 solutions.

Problems in Mathematics of KöMaL, September 2018