In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1/12 of a circle. Through how many radians do the minute hand and the hour hand move between 1:00 p. m. and 6:45 p. m. (on the same day)?

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  12 11/24 radians (combined angular motion)

Step-by-step explanation:

In one hour, the combined angular motion is ...

  (2π)(1 +1/12) = 13π/6 radians

Then in the 5 3/4 hours between 1 pm and 6:45 pm, the angular motion of the two hands will total ...

  (23/4)(13π/6) radians = 299π/24 radians = 12 11/24 radians

Additional comment

Maybe you're asking for the separate motions.

  minute hand: 2π×5.75 = 11.5π radians

  hour hand: (π/6)×5.75 = 23π/24 radians

step-by-step explanation: