An analog clock (with an hour hand and a minute hand) is running fast. At noon, both the minute hand and the hour hand are in the same place. Exactly 63 minutes later, the hands meet again. How fast is the clock running? (Or, in other words, one hour on this clock is actually how long?)
Solution
Jared Latiolais earned 5 points for the first correct answer. Dr. Mark Goadrich had the best explanation:
The hands should cross 11 times in 12 hours. This means between each crossing should be 720 / 11 = 65 and 5/11 minutes. But ours took 63 minutes. We set up the ratio of 63:65+5/11::60:x and solve for x. So one hour takes 57.75 minutes.
I also received a correct answer from Paul Ottoway.