Mathematical and Physical Journal
for High Schools
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Problem K. 524. (December 2016)

K. 524. Andy's washing machine keeps the door locked for an additional 5 minutes after the washing program is finished: it can only be opened after this delay. Andy knows this, so he includes this period when he calculates washing times. When the machine displays that 90% of the program time has elapsed, Andy knows that 20% of the calculated washing time is yet to follow. How long is the washing program in minutes?

(6 pont)

Deadline expired on January 10, 2017.


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

Megoldás. Legyen \(\displaystyle x\) perc az Andi által számolt teljes idő. Ha az Andi által a mosásra szánt idő 20%-a van még hátra, akkor az eltelt idő \(\displaystyle 0,8x\). A mosás \(\displaystyle x-5\) percig tart, ennek a 90%-a telt le. Tehát felírható, hogy

\(\displaystyle 0,8x = 0,9 (x–5).\)

Rendezve:

\(\displaystyle 0,8x=0,9x-4,5,\)

\(\displaystyle 4,5=0,1x,\)

\(\displaystyle 45=x.\)

Tehát a mosógép programja 45-5=40 perces.


Statistics:

121 students sent a solution.
6 points:Amamou Martin, Balogh Bence, Bárdos Deák Botond, Benczik Ákos , Bérczi Péter, Bottlik Domonkos, Cseh Dániel, Csikós Patrik, Csótai Enikő, Demcsák Ágnes, Dombai Zétény, Drong Máté, Espán Márton, Falvay Júlia, Farkas Boróka, Fekete Gergő 0706, Gion Áron, Gombocz Péter, Györfi Bence, Juhász 315 Dorka, Karácsonyi Máté, Kis 194 Károly, Kiss 014 Dávid, Kovács 124 Kinga, Kovács 615 Dorina, Kovács Fruzsina Dóra, Kozák 023 Áron, Kreisz Bálint, Markó Gábor, Mendei Barna, Merkl Levente, Molnár Apollónia Kármen, Nagy Kristóf Gergő, Op Den Kelder Júlia, Pálfi Bálint, Rusvai Miklós, Sándor 111 Réka, Szebeni Domonkos, Szente Péter, Szirtes Botond, Tornyi Napsugár, Tóth 222 Tea, Unger Dénes, Urbán István, Varga-Balázs Kristóf, Vörös Zsófia.
5 points:42 students.
4 points:3 students.
3 points:2 students.
2 points:1 student.
1 point:6 students.
0 point:11 students.
Unfair, not evaluated:10 solutionss.

Problems in Mathematics of KöMaL, December 2016