+0

-1
180
4
+111

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 :(

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.

Jun 7, 2020
#4
+111
0

thank you guest!!

andrewstanells  Jun 8, 2020
#2
+111082
+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)

Jun 8, 2020
#3
+111
0

thank you!! that helped a lot :))

andrewstanells  Jun 8, 2020