13.097. The distance from $A$ to $B$ by railway is 88 km, while by river it is 108 km. The train from $A$ departs 1 hour later than the riverboat and arrives in $B$ 15 minutes earlier. Find the average speed of the train, given that it is 40 km/h greater than the average speed of the riverboat.
## Solution.

Let $x$ km/h be the speed of the train, and $x-40$ km/h be the speed of the steamer. The train was on the way for $\frac{88}{x}$ hours, and the steamer for $\frac{108}{x-40}$ hours. According to the condition, $\frac{108}{x-40}-\frac{88}{x}=1+\frac{1}{4}$, from which $x=88$.

Answer: 88 km/h.