A tourist in London looks up at the clock in Big Ben tower...

A tourist in London looks up at the clock in Big Ben tower and finds that it is exactly 8:00. When she looks up at the clock later, it is exactly 8:10. a. Through what angle of rotation did the minute hand turn? Through what angle of rotation did the hour hand turn? b. Make a table that shows different amounts of time, from 5 minutes to 60 minutes, in 5-minute increments. For each number of minutes, provide the angle of rotation for the minute hand of a clock and the angle of rotation for the hour hand of a clock.

Transcript

00:01 So for this problem, we're told that a tourist looks at big ben and they see the clock go from 8 o 'clock exactly to 8 .10.

00:14 And the question is, how far did the minute hand move and how far did the hour hand move? so to calculate this, we need to think about a clock and in one hour, what does the minute hand do? well, in one hour, the minute hand goes all the way around the clock.

00:38 So the minute hand goes 360 degrees in one hour, right? and we know that one hour is actually equal to 60 minutes.

00:52 So it goes 360 degrees in 60 minutes.

01:01 If we divide that, we get six degrees per minute for the minute hand.

01:10 So in the 10 minutes from 8 to 810, the minute hand would have gone 10 times 6 degrees or 60 degrees.

01:23 The hour hand, on the other hand, goes 360 degrees in 24 hours.

01:33 And if we realize that there's one hour for every 60 minutes, we can do this math and find out how far, how far the hour hand goes per minute.

01:51 So we would take 360 divided by 24, and then we'd take that answer and divide by 60.

01:57 So in this case, the hour hand goes 0 .25 degrees per minute, and that's the hour hand.

02:10 So in 10 minutes, it would go 0 .25 degrees per minute.

02:19 If we multiply that, we would find out that we get 2 .5 degrees, per 10 minutes, which makes sense because the hour hand moves much more slowly.

02:33 So from 8 to 810, the minute hand of big bend would go 60 degrees and the hour would go 2 .5 degrees.

02:41 Now then we're asked to make a table on how many degrees through the both hands rotate in five minute increments.

02:59 So we're going to start at the zero, and then we're going to go to 05, 10, 15, 20.

03:15 This is going to be kind of a long table.

03:24 And these are going to be the number of degrees from 12.

03:44 So in one hour, it's going to be how many degrees does the minute hand move from the start of the hour to the end of the hour? we're going to have two columns.

03:56 We're going to have our minute hand column and our hour hand...

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