Question on Clock and Timings

Topic: Clock Word Problem

Question : Sam left Albert ville at x minutes past 6:00 am. He reached Carlton at y minutes past 6:00 am. He noticed that at both the beginning and the end of the trip the minute hand made the same angle of 110 degrees with the hour hand on his watch. How many times did it take Same to go from Albert ville to Carlton?

Answer :
When the minute hand makes a complete rotation of 360 degrees,
the hour hand advances 30degrees.
The time taken for the trip = (y-x) minutes.
The advance made by the hour hand during this period
of (y-x) minutes= (y-x) * 30/360 = (y-x)/12 degrees.
The advance made by the minute hand during this period = (y-x) * 6 degrees.
The angle between the two hands = The advance made by the minute hand – the advance made by the hour hand - 110= (y-x) * 6 – (y-x)/12 - 110 = 110 degrees
(y-x) (71/12) = 220
Hence y-x = 220 * (12/71) = 37.18 minutes when rounded to hundredth’s decimal.

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