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Shortly after 10 'o clock, the hands of a clock made a 90 degree angle. What's the time?

 Jun 16, 2021
 #1
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Shortly after 10 'o clock, the hands of a clock made a 90-degree angle. What's the time?

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60 - x/12 + x = 90          x = 328/11 degrees       ( x = 360 / 11 )surprise

 

 Jun 17, 2021
 #2
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At 10 o'clock the hour and minute hands are 60 degrees apart.

In one minute the minute hand advances \(\frac{1}{60}(360)=6\) degrees.

The hour hand, on the other hand (lots of puns that should be intended), advances \(\frac{1}{60}(30)=0.5\) degrees.

So the angle between the two hands increases by \(6-0.5=5.5 \)degrees per minute.

We are looking for the time when the angle is 90 degrees, that is when the angle has increased by 30 degrees.

It takes \(\frac{30}{5.5} \)or approximately 5.45 minutes for that to happen. So the two hands are at precisely 5 minutes and 27 seconds after 10  perpendicular to each other.

 Jun 17, 2021

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