Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 265. (November 2010)

K. 265. A man commutes to work by train. Every day in the afternoon, he arrives to the railway station with the same train, and his wife drives him home. The wife leaves home just in time to arrive at the station when her husband's train comes in. One day, the man arrived at the station an hour earlier, and started to walk home along the road on which his wife drove him home every day. The wife left home at the usual time. When she saw her husband on the road, she immediately stopped, picked him up and turned around. They arrived home 20 minutes earlier than usual. Calculate the time in minutes that the husband walked along the road.

(6 pont)

Deadline expired on December 10, 2010.


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

Megoldás. Ha 20 perccel hamarabb érnek haza, akkor történhett volna az is, hogy 20 perccel korábban indulnak autóval az állomásról. Azt is mondhatjuk, hogy ha a férfi felesége 20 perccel korábban elindul hazafelé az állomásról, de 10 perc múlva visszafordul és visszahajt az állomásra, majd onnan egyből hazamegy, akkor a szokásos időben érkezik meg. Ez azt is jelenti, hogy ha 10 percnyi autóútnyira találkoznak össze az állomástól, akkor fognak 20 perccel hamarabb hazaérkezni. Ezért a férfi 50 percet gyalogolt.


Statistics:

155 students sent a solution.
6 points:78 students.
5 points:15 students.
4 points:10 students.
3 points:1 student.
2 points:11 students.
1 point:7 students.
0 point:21 students.
Unfair, not evaluated:12 solutions.

Problems in Mathematics of KöMaL, November 2010