## Task 3 - 230523

The three pioneers Hans, Karl, and Peter rode their bicycles from Leipzig to Halle. Hans rode 2 kilometers in every 10 minutes, Karl needed 10 minutes for every 2.5 kilometers, while Peter covered 3 kilometers in every 10 minutes and reached Halle exactly 100 minutes later.

How many minutes after Peter did Hans and Karl arrive in Halle, if all three pioneers left Leipzig at the same time?
If Peter covers $3 \mathrm{~km}$ in 10 minutes, then in 100 minutes he covers ten times as much, which is 30 $\mathrm{km}$.

If Hans needs 10 minutes for $2 \mathrm{~km}$, then for $30 \mathrm{~km}$ he needs fifteen times as much, which is 150 minutes.

If Karl needs 10 minutes for $2.5 \mathrm{~km}$, then for $5 \mathrm{~km}$ he needs 20 minutes, so for $30 \mathrm{~km}$ he needs 120 minutes.

Since $150-100=50$, Hans thus arrived 50 minutes later than Peter in Halle. Since $120-100=20$, Karl arrived 20 minutes later than Peter in Halle.