[ Inequalities. Case Analysis ] [ Examples and Counterexamples. Constructions ]

Auto: : Akhinova **M. A**.

Vasya stood at the bus stop for some time. During this time, one bus and two trams passed by. After some time, Spy came to the same stop. While he was there, 10 buses passed by. What is the minimum number of trams that could have passed during this time? Both buses and trams run at equal intervals, with buses running at an interval of 1 hour.
Let's first provide an example when four trams passed during the Spy's observation: let buses run at 9:00, 10:00, ..., and trams run with an interval of 1 hour 58 minutes - at 10:01, 11:59, 13:57, 15:55, 17:53, 19:51, 21:49, ... Then Vasya could stand from 10:01 to 11:59, and the Spy could observe from 12:00 to 21:00.

Estimation. Vasya stood at the bus stop for less than two hours (since only one bus passed). Therefore, the interval between trams is less than two hours.

The Spy observed for at least 9 hours, so more than 7 hours passed after the first tram appeared, during which at least three more trams passed. Therefore, the Spy saw at least four trams.

## Answer

4 trams.

## Problem