A cargo ship departs from Balatonalmádi at 7:00 AM heading to Keszthely, and a cruise ship leaves Keszthely at 9:00 AM heading to Almádi. They meet at 1:00 PM. After passing each other, they continue their journeys. The cruise ship arrives at Almádi 12 minutes earlier than the cargo ship arrives at Keszthely. When does the cruise ship dock in Almádi?
I. solution: Consider the Almádi - Keszthely route segment as a unit. The cruise ship reaches the meeting point in 4 hours and continues for another $x$ hours until it arrives in Almádi, so its speed is $\frac{1}{x+4}$ units/hour.

The cargo ship reaches the meeting point after 6 hours of travel and then needs another $x+0.2$ hours to reach Keszthely, so its speed is $\frac{1}{x+6.2}$ units/hour.

By the time of the meeting, together they have covered exactly the unit distance, that is,

$$
\frac{4}{x+4}+\frac{6}{x+6.2}=1
$$

Removing the fractions and rearranging,

$$
x^{2}+0.2 x-24=0
$$

from which

$$
x_{1}=4.8, \quad\left[x_{2}=-5\right]
$$

Thus, the cruise ship arrives in Balatonalmádi at $13+4.8=17.8=17$ hours and 48 minutes.

Tamás Rázga (Bp., II., Rákóczi g. II. o. t.)

II. solution: Let the travel time of the cruise ship from the meeting point to Almádi be $x$ hours. The cargo ship covered this distance in 6 hours, and the remaining distance to Keszthely in $x+0.2$ hours. For the cruise ship, this latter segment took 4 hours. The times spent on the respective segments are proportional, that is,

$$
x: 6=4:(x+0.2)
$$

which means

$$
x^{2}+0.2 x=24 \text { etc. }
$$

as in the first solution.

Ildikó Barabás (Nyíregyháza, Zrinyi Ilona lg. II. o. t.)