1.1. A group of tourists set out on a route from a campsite. After 15 minutes, tourist Ivan remembered that he had forgotten a flashlight at the campsite and went back for it at a higher speed than the main group. After picking up the flashlight, he started to catch up with the group at the same increased speed and did so only 2.5 hours after he left to get the flashlight. Assuming the speeds of the group and Ivan outside the group are constant, find how many times Ivan's speed is greater than the group's speed. Write the answer as an integer or a decimal.
# Answer: 1.2

Solution. Let the distance Ivan and the group walked in 15 minutes be $x$. Then in 2.5 hours, which is 150 minutes, the group without Ivan walked $10 x$. In the same time, Ivan had to walk $12 x$, as he walked the same distance as the group and twice the distance $x$ that separated him from the forgotten flashlight. Thus, in the same amount of time, Ivan walked $12 x / 10 x = 1.2$ times more, meaning his speed was that much greater.