## 11. Polar Expedition

A polar explorer set out from one point to another on a sled pulled by a team of five dogs. But after 24 hours, two of the dogs died, causing the explorer's speed to decrease to $3 / 5$ of the original speed, and he was delayed by two days.

- Oh! - exclaimed the polar explorer. - If the two dogs that died had run another 120 km, I would have been delayed by only one day.

What distance did the polar explorer travel?
11. If two dogs had run 120 km more, the polar explorer's delay would have been reduced by 24 hours (48-24). Therefore, if these dogs had run 240 km further, the polar explorer's delay would have been 48-24-24=0 hours, i.e., he would have arrived on time; hence, the distance from the place where the dogs fell to the destination is 240 km. Let $v$ be the initial speed of the polar explorer. From the moment the dogs fell until arrival at the destination, the time taken is

$$
48+240 / v, \text { or } 5 / 3 \cdot 240 / v .
$$

Therefore,

$$
48+240 / v=400 / v, \quad \text { i.e., } \quad v=10 / 3 \text{ km} / \text { h. }
$$

Before the dogs fell, the polar explorer had traveled (in 24 hours)

$$
24 \cdot 10 / 3=80 \text{ km}
$$

Thus, the total distance is

$$
80+240=320 \text{ km. }
$$