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#### paulmdrdo

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- May 13, 2013

- 386

if the hour hand of a clock has a length of 4 in. how far does its tip travel in 1hr and 20min?

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- May 13, 2013

- 386

if the hour hand of a clock has a length of 4 in. how far does its tip travel in 1hr and 20min?

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- #2

- Feb 7, 2012

- 2,785

The tip of the hour hand travels round a circle of radius 4 in, covering a complete revolution in 12 hours. You know the formula for the circumference of the circle. So what fraction of that will be be covered in 1hr 20 min?if the hour hand of a clock has a length of 4 in. how far does its tip travel in 1hr and 20min?

- Aug 7, 2013

- 21

$\displaystyle\frac{2\pi}{12\text{ hr}}=\frac{a}{1\text{ hr and }20\text{ min}}$

"a" is the angle in radian that would be generated in time 1hr and 20 min. - convert the minute part into hour.

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- May 13, 2013

- 386

can you please explain further. anyone who's online please i want an urgent answer. thanks!

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- #5

\(\displaystyle s=r\theta\)

We are given the radius $r=4\text{ in}$, and the angle $\theta$ can be determined from the elapsed time. The hour hand makes a complete revolution in 12 hours, and a complete revolution is $2\pi$ radians. What fraction of 12 hours is 1 hour and 20 minutes? When you find this fraction, which represents the fraction of a complete revolution the hour hand makes, then multiply this fraction by the complete revolution to find the angle through which the hour hand turns in the given time.

So, how many hours is 1 hour and 20 minutes?

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- May 13, 2013

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- #8

- May 13, 2013

- 386

4/3/12 = 16 is this right?

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- #9

- Feb 7, 2012

- 2,785

No. 4/3 divided by 12 is $\dfrac4{3\times12}$.4/3/12 = 16 is this right?

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No, we want:4/3/12 = 16 is this right?

\(\displaystyle \frac{4/3}{12}=\frac{1/3}{3}=\frac{1}{3\cdot3}\)

We know that 4/3 is smaller than 12, so when we divide 4/3 by 12, we should expect to get a fraction smaller than one.

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- #11

- May 13, 2013

- 386

but i have a follow up question why is ratio and proportion also works in this problem?

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- #12

\(\displaystyle s=\frac{8\pi}{9}\text{ in}\)

Using proportions, which is quite similar to what we've just done, we may state in words:

12 hours is to one revolution what 4/3 hours is to some part of a revolution. Stated mathematically, this is:

\(\displaystyle \frac{12\text{ hr}}{2\pi}=\frac{\frac{4}{3}\text{ hr}}{\theta}\)