Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem B. 3892. (March 2006)

B. 3892. The president of the Pyramid Bank lives in a fancy residential district outside the city. On weekdays, he is driven to the city in a car that leaves the bank in the city at the same time every morning, picks up the president and they arrive at the bank exactly when it opens. One morning, the driver called the president to say that something was wrong with the car and he would be late. So the president left home one hour earlier than usual on foot. Meanwhile, the driver fixed the car and still managed to leave the city at the usual time. He met the bank president on the way, picked him up, and they arrived at the bank 20 minutes before opening. How long did the president walk? (Assume that the speed of the car is constant, and picking up a passenger does not take any time.)

(3 pont)

Deadline expired on April 18, 2006.

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

Megoldás: A sofőrnek az oda-vissza út a szokásosnál 20 perccel rövidebb ideig tartott, egy irányban tehát 10 perccel volt rövidebb az útja. Ezek szerint a megszokott időpontnál 10 perccel hamarabb találkozott az elnökkel. Minthogy pedig az elnök a megszokott időpontnál 60 perccel hamarabb indult otthonról, 50 percet kellett, hogy gyaloglással töltsön.


164 students sent a solution.
3 points:127 students.
2 points:13 students.
1 point:8 students.
0 point:15 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, March 2006