## Task 3 - 190623

A total of 110 hours is planned for the installation of a device. The installation will be carried out in three stages.

For the second stage, exactly three times as much time is planned as for the first; the third stage is to last exactly half as long as the second.

Determine the times to be planned for each individual stage according to this!

Check whether these times meet all the given requirements!
If the requirements are met and the first section takes $x$ hours, then the second takes $3 x$ hours and the third $\frac{3}{2} x$ hours. From this, it follows that

$$
x+3 x+32 x=110 \quad \rightarrow \quad x=20
$$

Thus, the requirements can only be met by planning 20 hours for the first section, and therefore 60 hours for the second and 30 hours for the third.

These times meet the requirements; because 60 hours are three times as much time as 20 hours, 30 hours last half as long as 60 hours, and since $20+60+30=110$, the planned total time is achieved.