## 1190.32 – The Phone Booth

You are on a scavenger hunt, following clues here and there around the city. At this moment your watch says 1:30 pm, but at the moment it is 20 minutes slow. Not only that, it is losing 10 minutes every hour after a bus ran over it last week. You must be in the phone booth at 6th Avenue and 44th street at exactly 4:00 to receive a call with at your next clue. If you don't reset your watch between now and then, at what time by your watch should you be at the phone booth?

## Solution

This is messy. Let's see: right now it is really 1:50. That is 2 hours and 10 minutes before 4:00, or 2$\frac{1}{6}$ hours, or $\frac{13}{6}$ hours. In that time your watch will lose $\frac{13}{6}$ x 10 minutes more, or 21$\frac{2}{3}$ minutes.

This means that the real time of 4:00 your watch will be 20 + 21$\frac{2}{3}$ slow, i.e. 41 minutes 40 seconds slow. So you should show up that much early by your watch, namely 3:18:20. 3:18:20 + 41:40 = 4:00. Whew. You need to get your watch fixed, or replace it.