Mathematical and Physical Journal
for High Schools
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Problem K. 146. (December 2007)

K. 146. Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs. In this way she takes 20 minutes to get there. On her way home, she runs for twice the length of time as she walks. How long does she take to get home?

(6 pont)

Deadline expired on January 10, 2008.

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

Megoldás. Mivel kétszer olyan gyorsan fut, mint sétál, ezért az iskolába menet a fele távot sétálva (40/3 perc alatt), a fele távot futva (20/3 perc alatt) tette meg. A teljes távot sétálva tehát 80/3 perc alatt, futva 40/3 perc alatt tenné meg. Hazafelé négyszer akkora távot tett meg futva, mint sétálva, ezért a teljes táv 4/5 részét futotta le (40/3.4/5=32/3 perc alatt), a táv 1/5 részét pedig sétálva tette meg (80/3.1/5=16/3 perc alatt). Így összesen 48/3, azaz 16 percig tartott a hazafelé vezető útja.


182 students sent a solution.
6 points:136 students.
5 points:3 students.
4 points:2 students.
3 points:10 students.
2 points:7 students.
1 point:7 students.
0 point:9 students.
Unfair, not evaluated:8 solutions.

Problems in Mathematics of KöMaL, December 2007