Answer to Question #237431 in Algebra for Mr. Lee

Question

After how many minutes from 12:00 o’clock noon will the

minute hand and the hour hand of the clock makes and

angle of 120degrees for the first time.

Answer 1

Let x = position of the minute hand (in minutes) when this occurs.

The minute hand travels 360 degrees in 1 hr

The hr hand travels $\frac {360} {12}$ = 30 degrees, in 1 hr

The fraction of an hr can be expressed by $\frac {x} {60}$

Min hand degrees - hr hand degrees = 120

$(\frac {x} {60})×360-(\frac {x} {360}) ×30=120$

$6x - 5x = 120$

$5.5x = 120$

$x = \frac {120} {5.5}$

$x$ = 21.82 minutes or 21 min 49 sec