The clock face on London’s Big Ben measures 23 feet across. How far does the tip of the minute hand travel between 6:50 and 7:30?

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Veasley2004 Veasley2004

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Advanced Placement (AP)

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The clock face on London’s Big Ben measures 23 feet across. How far does the tip of the minute hand travel between 6:50 and 7:30?

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MrRoyal MrRoyal · Answer 1 · 2025-04-23T20:22:13-04:00

Answer:

The distance traveled is: 96.29ft

Explanation:

Given

[tex]r = 23ft[/tex] --- The minute hand represents the radius

Required

Distance traveled between 6:50 and 7:30

First, calculate the circumference (C) of the clock

[tex]C = 2\pi r[/tex]

[tex]C = 2*3.14*23[/tex]

[tex]C = 144.44ft[/tex]

Calculate the time difference between 6:50 and 7:30

[tex]t = 7:30 - 6:50[/tex]

[tex]t = 40\ minutes[/tex]

Next, calculate the rate per 60 minutes:

[tex]Rate = \frac{C}{60\ minutes}[/tex]

So, the distance traveled is:

[tex]d = Rate * t[/tex]

[tex]d = \frac{C}{60\ minutes} * t[/tex]

[tex]d = \frac{144.44ft}{60\ minutes} * 40\ minutes[/tex]

[tex]d = \frac{144.44* 40ft}{60}[/tex]

[tex]d = \frac{5777.6ft}{60}[/tex]

[tex]d = 96.29ft[/tex]