Clock Problem

Geometry Level 2

In how many minutes after 6 o'clock will the hands of the clock next be directly opposite with each other again?

Image credit: Wikipedia Inisheer

The answer is 65.45.

4 solutions

Arup Saha
Aug 13, 2014

In 60 min, the minute hand completes 360 degrees, so in 1 min, the minute hand completes -> 6 degrees (1)

Smilarly, in 12 hours (ie 12 * 60 minutes), the hour hand completes 360 degrees, so in 1 min, the hour hand completes -> 0.5 degrees (2)

At 6 o'clock, the minute hand is at 0 degrees and hour hand is at 180 degrees

Let's say after x minutes, the minute and hour hand are completely opposite (i.e. have an angle of 180 degrees between them)

so from (1) and (2)

6x +/- (180 + 0.5x) = 180

the solution to this equation is x = 0 and x = 360/5.5

So the answer is x = 360/5.5 (i.e. 65.454545...)

as x = 0 suggests that it is 6 o'clock only

Saya Suka
Apr 24, 2021

In 1 day, the clock hands will form 180° together 22 times.

Answer
= 24 × 60 / 22
= 720 / 11
= 65.45 minutes

Sam Cheung
Aug 6, 2014

The next time they will be opposite each other will be 7:05.

This is very easy, it's not a level 2 problem.

Sam Cheung - 6 years, 10 months ago

Vishal Bhosale
Aug 1, 2014

check perfect angle 180

The minute hand is moving at $v_m=12\text{ units/hr}$ , the hour hand is moving at $v_h=1\text{ unit/hr}$ , where a unit is the 5 minute distance of the minute hand. The minute hand is moving at $v=11 \text{ units/hr}$ relatively to the hour hand, and it'll travel 12 units relatively to the hour hand in $\frac{12}{11}\approx 1.09 \text{ hr}\approx 65.45 \text{ minutes}$ .

mathh mathh - 6 years, 10 months ago

in short you can just use a formula and that would be Time = (2/11)(Angle Reference +/- Final Angle)

joram otero - 6 years, 10 months ago

its not correct 180

gautam sachdeva - 6 years, 10 months ago

Clock Problem

Image credit: Wikipedia Inisheer

The answer is 65.45.

4 solutions

0 pending reports