## Task 6 - 240836

Two motorcyclists undertake a trip, during which both cover the same distance. They start at the same time and arrive at the destination simultaneously. Rider $A$ takes twice as much time to drive as $B$ takes to rest. Rider $B$, on the other hand, drove three times as long as $A$ rested.

Which of the two riders had the longer rest period?
If the rest time of A is denoted by $a$ and that of B by $b$, then the (pure) driving time for A is $2 b$ and for B it is $3 a$. Since the sums of driving time and rest time are equal for both drivers, we have

$$
a+2 b=b+3 a \quad \text { so } \quad b=2 a>a
$$

Thus, driver B had the longer rest time.

Solutions of the third round 1984 adopted from [5]

### 5.27 XXV. Olympiad 1985

### 5.27.1 First Round 1985, Class 8