Evokimov M.A.
By the river, there lives a tribe of Mumbo-Jumbo. One day, with urgent news, a young warrior Mumbo and a wise shaman Yumbo set out simultaneously for the neighboring tribe. Mumbo ran at a speed of 11 km/h to the nearest raft storage and then sailed on a raft to the neighboring tribe. Meanwhile, Yumbo, without hurrying, walked at a speed of 6 km/h to another raft storage and then sailed to the neighboring tribe from there. In the end, Yumbo arrived before Mumbo. The river is straight, and the rafts float at the speed of the current. This speed is the same everywhere and is expressed as an integer km/h, not less than 6. What is the greatest possible value of this speed?
Let the habitat of the Mumbo-Jumbo tribe be denoted by $O$, the storage that Mumbo ran to by $M$, and the storage that Jumbo went to by $U$. Clearly, $M$ is located upstream from $O$, and $U$ is downstream. Let the distances from $O$ to $M$ and $U$ be $x$ and $y$ km, respectively

$(x<y)$, and the speed of the river be $v$ km/h. The time it took Jumbo to travel from $O$ to $U$ was $y / 6$ hours, and Mumbo took $-x / 11 + (x + y) / v$ hours. Since Jumbo arrived at $U$ before Mumbo, we have $y / 6 < x / 11 + (x + y) / v < y / 11 + 2y / v$. Dividing by $y$ and transforming, we get $v < 26.4$.

It remains to check whether the speed of the river could have been 26 km/h. For this, in the inequality $y / 6 < x / 11 + (x + y) / v$, let $v = 26$ and transform it equivalently to the form $y / x < 111 / 110$. The latter is possible (for example, when $y = 1.12$ km, $x = 1.11$ km).

## Answer

26 km/h.