Answer to Question #237432 in Algebra for Mr. Lee

Question #237432

At what time after 12:00 o’clock midnight will the minute

hand and the hour hand of a clock be on a straight line for

the first time?


1
Expert's answer
2021-09-20T16:44:43-0400

Since the Complete Angle is "360^{\\circ}"; therefore, the minute hand travels "360^{\\circ}"in one hour.

The clock is divided into "12" parts (hour); therefore, the hour hand travels "\\frac{360^{\\circ}}{12}=30^{\\circ}" in one hour.

Let "x" be the position of the minute hand on the clock (in minutes)

Since one hour has "60" minutes; therefore, one hour can be expressed as "\\frac{x}{60}".

So to find the position of the minute hand on the clock substitute into the relation:

Min hand in degrees - Hour hand in degrees = "180^{\\circ}"

"\\frac{x}{60}\\cdot 360-\\frac{x}{60}\\cdot 30=180^{\\circ}"

Simplify each fraction:

"6x-\\frac{1}{2}x=180"

Subtract the terms:

"5.5x=180"

Divide both sides by "5.5" :

"x\\approx 32.73"

So, at "12:32:73" both pm, the hands of a clock will be in a straight line.


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