Question

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)?

Short answer

The angle that is moved by the minute hand in 1hr is 36.128 radians and the angle that is moved by the hour hand is 3.0107 radians.

Step-by-step solution

Step 1. Given Information.

In 1 hr the minute hand on a clock moves through a complete circle, and the hour hand moves through$\frac{1}{12}$of a circle.

In 1 hr, hour hand move$\frac{2\pi }{12}$radian and minute hand move$2\pi$radian.

The time between 1:00 p.m. and 6:45 p.m. is 345 minutes.

Step 2. Determining the values.

Total time $t=345$minutes

The angle moved by minute hand in 1 hr is$2\pi$ radian

Thus,

The angle moved by minute hand in 345 minutes is $=\frac{2\pi }{60}\times 345$radian

$=36.128$radian

The angle moved by hour hand in 1 hr is $=\frac{2\pi }{12}$

$=\frac{2\times 3.14}{60}\times 345\times \frac{1}{12}$

$=3.0107$radians

Thus, these are the angles that is moved in 345 minutes.