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Problem K. 205. (March 2009)

K. 205. Jack and Jill are going to the gingerbread house 20 km from their home. The two of them have one bicycle together. The bicycle can only bear one rider at a time. They decide that Jack will walk first and Jill will go by bike to some point along the way where she puts the bike down and continues on foot. When Jack reaches that point, he will get on the bike and cycle to the gingerbread house. Jack's speed is 5 km/h on foot and 12 km/h by bike. Jill walks at 4 km/h and bikes at 10 km/h. If they start out together, how many kilometers should Jill cover by bike so that they get to the gingerbread house at the same time?

(6 pont)

Deadline expired on 10 April 2009.


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

Megoldás. Ha Juliska x km-t biciklizik, és 20–x km-t gyalogol, akkor \frac{x}{10}+\frac{20-x}{4} óra alatt ér el a házig. Ha Jancsi x km-t gyalogol, és 20–x km-t biciklizik, akkor ő \frac x5+\frac{20-x}{12} óra alatt ér el a házig. A két időtartam egyenlő, tehát \frac x5+\frac{20-x}{12}=\frac{x}{10}+\frac{20-x}{4}, rendezve az egyenletet x=12,5 km.


Statistics:

125 students sent a solution.
6 points:91 students.
4 points:1 student.
3 points:4 students.
2 points:6 students.
1 point:12 students.
0 point:3 students.
Unfair, not evaluated:8 solutions.

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