## Task 4 - 050514

Gerd, Fred, Heinz, and Werner are on their way to school. Fred is still three times as far away from the school as Gerd. Heinz has four times the distance left to the school that Gerd has to cover.

Werner still has to walk $2.4 \mathrm{~km}$ to the school; this is twice the length of Fred's distance.

a) What distances do the individual students still have to cover before they reach the school? b) How many minutes will pass until all students have arrived at the school, if each student takes exactly $90 \mathrm{sec}$ for every $100 \mathrm{~m}$?
a) Let the remaining distances to be covered by the students be \( f \) for Fred, \( g \) for Gerd, \( h \) for Heinz, and \( w \) for Werner. According to the problem statement, the following equations apply:

\[
f = 3g \quad(1) ; \quad h = 4g \quad(2) ; \quad w = 2.4 \text{ km} \quad(3) ; \quad w = 2f
\]

From (3) and (4), it follows that Fred's distance is 1.2 km. Thus, according to (1), Gerd has a remaining distance of 400 m to cover. Relationship (2) then gives Heinz a distance of 1.6 km.

b) Since Werner is the farthest away, the students will only meet when Werner arrives. For Werner, it holds that:

Werner needs for 2.4 km: \( 24 \cdot 90 \text{ s} = 2160 \text{ s} = 36 \text{ min} \).

Thus, it will take another 36 minutes for all the students to be in the class.