## Task 1 - 340621

A jogger needs 20 seconds for each $100 \mathrm{~m}$ in a steady run.

a) What distance can he cover if he maintains this pace for 20 minutes without change?

b) What distance can he cover if, in the total 20 minutes of running, there are also times when he needs 30 seconds for each $100 \mathrm{~m}$, and these times cover a total of 1600 $\mathrm{m}$?
(a) Since the jogger manages 100 m in 20 seconds and since 20 minutes is 60 times as much time as 20 seconds, he manages $60 \cdot 100 \mathrm{~m}=6000 \mathrm{~m}$ in 20 minutes.

(b) While he runs the $1600 \mathrm{~m}$ at the lower speed, he takes 16 times as much time as for $100 \mathrm{~m}$, so $16 \cdot 30$ seconds $=480$ seconds $=8$ minutes.

Since $20-8=12$, 12 minutes remain for the higher speed. Since a minute is 3 times as much time as 20 seconds, he manages $3 \cdot 12 \cdot 100 \mathrm{~m}=3600 \mathrm{~m}$ in these 12 minutes.

In total, he covers $1600 \mathrm{~m}+3600 \mathrm{~m}=5200 \mathrm{~m}$.