Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 841. (February 2006)

C. 841. Paul the postman was delivering letters in a long street. First he walked down the street on one side (where the odd-numbered blocks were) and then he walked back on the other side (delivering the letters to the even-numbered blocks). On the odd side he spent one third as much time standing in front of the letter boxes as he spent by walking back on the even side. On his way back on the even side his total standing time in front of the letter boxes was one third as much as his time in motion down the street on the odd side. Finally, it turned out that delivering the letters took the same time on each side. Find the ratio of his average walking speed (not counting the stops) on the odd side to his average walking speed back on the even side.

(5 pont)

Deadline expired on March 16, 2006.

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

Megoldás: Haladási idő oda: t1, állás idő oda: t2, haladási idő vissza: t3, állás idő vissza: t4, az utca hossza: s. Tudjuk, hogy t_2={1\over3}t_3, t_4={1\over4}t_1, t1+t2=t3+t4, ezért t_1+{1\over3}t_3=t_3+{1\over4}t_1, azaz t_3={9\over8}t_1. Átlagsebesség oda: v_{oda}={s\over t_1}, átlagsebesség vissza: v_{vissza}={s\over t_3}={s\over{9\over8}t_1}. Vagyis:

{v_{oda}\over v_{vissza}}={{s\over t_1}\over {s\over{9\over8}t_1}}={9\over8}.


321 students sent a solution.
5 points:217 students.
4 points:74 students.
3 points:8 students.
2 points:1 student.
1 point:1 student.
0 point:19 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, February 2006