# Convert time measurements to angles of movement

### Question:

A test began at 2:15 pm and ended at 3:50 pm. Through how many degrees had the minute hand turned? I got 570 degrees. The solution my prof provided is 545 degrees.

I think that is a typo -- is 570 actually the correct answer?

The minute hand takes exactly 1 hour to go around the clock, and during that revolution it covers 360 degrees. Therefore, the "speed" of the minute hand is 360 degrees per hour. How many hours are between 2:15pm and 3:50pm? There's 1 hour and 35 minutes, which can also be written as a mixed number as $$1\frac{35}{60}$$.
Now multiply that number times 360 degrees, and you get $$360 + 360*\frac{35}{60}$$. That equals 570, which is indeed the correct answer.