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12 o'clock
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right now?

The answer is 16.363.

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The absolute value sign turns $-11\text{min}$ into $11\text{min}$

Daniel Liu
- 6 years, 10 months ago

For every $60$ divisions the minute hand moves, the hour hand moves $5$ divisons.

So for every $12$ divisions the minute hand moves, the hour hand moves $1$ division.

If $x = hours$ , $y = minutes$ , then

$12x = y$

$\implies x = \frac{y}{12}$

For the hands to create a $90°$ , there must be $15$ divisions between them.

$\implies y - x = 15$

$\implies y - \frac{y}{12} = 15$

$\implies \frac{11 y}{12} = 15$

$\implies y = \frac{180}{11} = \boxed{16.363} minutes$

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Nice solution and your problem .

Shohag Hossen
- 5 years, 11 months ago

Why 15 divisions?

Mohamed mamdouh
- 7 years ago

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Let x be the angle.

As the Minutes Hand moves 6 degree (360/60) in a minute and the Hours Hand moves 0.5 Degree(360/(60*12), so the Equation will be

x

6-x.5=90x(6-.5)=90

x=90/5.5

boxed $x=16.363636$

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$\frac{|60h-11m|}{2} =Angle$ Since the given angle is 90 degree substituting that and o for the hour since 12 hrs is 0 we get $\frac{|60(0)-11(min)|}{2}=90$ We get $180=-11min$ dividing by -11 we get -16.36 but we cannot have negative min so the answer is simply $16.3636$ minutes. I don not know if this is possible solution.