What is the first time after 1pm at which the minute hand and hour hand of a clock point in **exactly** opposite directions?

Hint: 147

thank u guys in advance :)) also, i don't know what the hint means :(

andrewstanells Jun 7, 2020

#1**+2 **

I think you mean when they are 180 degrees apart:

180=abs((30*1) - (5.5*M)), solve for M

M =420 / 11 =38.181818........minutes - or 38 minutes and about 11 seconds after 1 O'clock.

Guest Jun 7, 2020

#2**+2 **

Just thinking about it logically I can see that this will happen between 1:35 and 1:40 So any calc I do can be checked against this.

The hour hand starts 30 degrees past the hour and the minute hand starts on the hour.

After 1 minute the hour hand travels 0.5 degrees and the minute hand travels 6 degrees

so

After x minute the hour hand travels 0.5x degrees and the minute hand travels 6x degrees

the hour hand starts on the 1 so it has that 30 degrees 'head start'

The angle between for the first half hour of so will be 6x-(30+0.5x) and we want that equal to 180

Solve the equation and we get x= \(38\frac{2}{11}\;\;minutes\)

So at \(38\frac{2}{11}\;\;minutes\) past 1 the hands will be exactly opposite each other.

(just as our guest already determined. - thanks guest)

Melody Jun 8, 2020