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A worker noticed that the hour hand on the factory clock had moved by $225$ degrees during her stay at the factory. For how long did she stay in the factory?

  1. $3.75$ hours
  2. $4$ hours and $15$ mins
  3. $8.5$ hours
  4. $7.5$ hours
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Migrated from GO Mechanical 4 years ago by Arjun

2 Answers

Best answer
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9 votes

Hour hand of a clock covers $360^{\circ}$ in $12$ hours.

Since, $360^{\circ}$ is covered in $12$ hours. So, $225^{\circ}$ will be covered in $\frac{225^{\circ}}{360^{\circ}}\times12 = 7.5$ hours.

So, Answer is (D)

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Number of hours in a clock $= 12$ hours

One rotation hour hand covers $360^{\circ} $

$360$ degrees $= 12$ hours

$1$ degree $=\dfrac{12}{360}$ hours

$225$ degrees $=\dfrac{12}{360}\times 225$ hours $=7.5$ hours

                                                                                    $(OR)$

The worker stays in the factory $=3\ hours \ ({0^{\circ} \ to \ \ 90^{\circ}}) +3 \ hours  \ ({90^{\circ} \ to \ \ 180^{\circ}}) +\dfrac{3}{2}\ hours \ ({180^{\circ} \ to \ \ 225^{\circ}}) = 7.5 \ hours$

So, option $(D)$ is the correct choice.

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