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At 3:17, what is the difference in degrees between the hour hand and minute hand?

Theo Osifeso wrote:At 3:17, what is the difference in degrees between the hour hand and minute hand?

The two answers that popped into my head were........

I don't know, I own digital clock

.......and zero, or close to it :king:

3.5

I got 3.5, too. Although I bet there is an interpretation of "difference in degrees" that changes the question from the obvious.

interesting so far ...

What's the one easy mistake to avoid in solving this problem?

Theo Osifeso wrote:At 3:17, what is the difference in degrees between the hour hand and minute hand?

• temp: same temperature.
• angle: looking from the side, there is no difference.

Michael Smith wrote:

Theo Osifeso wrote:At 3:17, what is the difference in degrees between the hour hand and minute hand?

• temp: same temperature.
• angle: looking from the side, there is no difference.

Hours and minutes, so we are talking angles and there is a difference. Now answer the question before I come down to your office

Theo Osifeso wrote: Hours and minutes, so we are talking angles and there is a difference. Now answer the question before I come down to your office

Equation for the degrees on the hour hand
(0.5 degrees per minute on the hour hand) * (the time on the hour hand * 60 minutes per hour) + (0.5 degrees per minute on the minute hand) * (the time on the minute hand)

Equation for the degrees on the minute hand
(6 degrees per minute on the minute hand) * (the time on the minute hand)

3.5 assumes it's a standard 12 hour analog clock with hands that rotate continually and at a constant rate, and that the second hand is at 12. I supposed the easy mistake to make is to calculate the answer with the hour hand pointed at the 3, rather than 17/60ths of the way to 4.

Unless there is some major trick question twist to this one, I agree with Jeff and Will.

(17mins/60mins)*360 degrees = 102 degrees (position of min hand)
((17mins/60mins)+3hours)/12 hours)*360 degrees = 98.5 degrees (position of Hour hand)
102 -98.5 = 3.5 degrees

are we still missing something?

Obviously could be 356.5°, too.

Jeff Stuart wrote:3.5 assumes it's a standard 12 hour analog clock with hands that rotate continually and at a constant rate, and that the second hand is at 12. I supposed the easy mistake to make is to calculate the answer with the hour hand pointed at the 3, rather than 17/60ths of the way to 4.

That's what can be missed

Christine Berry wrote:Unless there is some major trick question twist to this one, I agree with Jeff and Will.

(17mins/60mins)*360 degrees = 102 degrees (position of min hand)
((17mins/60mins)+3hours)/12 hours)*360 degrees = 98.5 degrees (position of Hour hand)
102 -98.5 = 3.5 degrees

are we still missing something?

Nope. You explained it perfectly

OK, a related question.... how much time passes between each crossing of the hour and minute hand? No tricks - standard 12-hour clock, etc. Explain how you got your answer.

The two hands will cross 11 times over the course of 12 hours, so

((12 hours)*(60 minutes/hour)/11 = 65.4545... minutes = 1 hour, 5 minutes, 27.27272727... seconds.

Jeff Stuart wrote:The two hands will cross 11 times over the course of 12 hours, so

(12 hours)/(11 times) = 65.4545... minutes = 1 hour, 5 minutes, 27.27272727... seconds.

Are you some sort of genius?

Nicely done.

Theo Osifeso wrote: Are you some sort of genius?

Nicely done.

Heh, I like word problems, and doing these is more entertaining than work right now, unfortunately.

I got 3.5 and I went to a Liberal Arts school.

Steve Ekstrand wrote:I got 3.5 and I went to a Liberal Arts school.

But, I bet you got 3.5 right after Will did the work----

Don

Nope, I didn't scroll. Liberal Arts taught me the value of living on a path of learning and discovery. It does help that I have an old fashion school style clock staring at me on the desktop.

But after the Liberal Arts School, then I went to Business School and to Law School. Both taught me that its far simpler to just profit from the work of guys like Will.

Sunpower uses that one as a filter to automatically reject job applicants.

John Stimson wrote:Sunpower uses that one as a filter to automatically reject job applicants.

That doesn't seem fair.

But then the interview for my current job was the interview from hell. 9 hours of grilling in one day by 10 people and they all have to like you. I hated all of them by the end of the day but now we are all good friends.

Jeff Stuart wrote:The two hands will cross 11 times over the course of 12 hours, so

((12 hours)*(60 minutes/hour)/11 = 65.4545... minutes = 1 hour, 5 minutes, 27.27272727... seconds.

You got it. Many people will say "an hour", then say "oh, wait, an hour and 5 minutes", then I tell them that in that five minutes the hour hand will have moved a little more and in that time a little more and so on and on. Some people will take the bait and keep going on that path. That's where we transition from math into comedy }:)

I like to play those jokes on liberal arts grads. Later in life, you find that a little wrench twirling and they give you a co-drive seat and boot themselves out of the trophies. }:) :gpower:

George Schilling wrote:

Theo Osifeso wrote:At 3:17, what is the difference in degrees between the hour hand and minute hand?

The two answers that popped into my head were........

I don't know, I own digital clock

.......and zero, or close to it :king:

i'm with george on this one...i barely know how a dial clock works. My hour and minutes are on the same plane of lcd on my cellphone.

for the record, I failed. assumed 90deg for 3 o'clock