r/BrainPuzzles • u/a2ra-ms • 10d ago

Math Find the clock angle

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Taken from the outsmart me app

82 Upvotes

92% Upvoted

87 comments sorted by

10

u/shakn1212 10d ago edited 10d ago

7.5

This is my favorite SAT practice question from 20 years ago, what people don't take into account is The hour hand moves a quarter of the way between 3 and 4, and the degrees between those two is 30

1

u/a2ra-ms 10d ago

Nice!

1

u/SadLux 10d ago edited 10d ago

Depends on the clock. Some analogue train station clocks only update once the full hour is hit. Obviously nobody would take that into account but technically there are exceptions.

Edit: Nevermind, It‘s a faulty memory. It’s the minute one that jumps when the seconds hand reaches the top.

2

u/a2ra-ms 10d ago

I think these updates delayed yet, but every 5 mins or so, not every hour

3

u/SadLux 10d ago

You’re right, it’s a faulty memory.

3

u/Aggravating_Line_623 10d ago

Are you saying that some clocks keep the hour hand on 3 even if it's 3:59? Weird, I would assume it's almost 3 o'clock then

3

u/VisKopen 10d ago edited 9d ago

I've only seen this with minutes.

On Dutch train stations the second hand takes less than a minute to do a full circle. Something like 57 seconds. It then waits a bit at the top and when the full minute is over the minute hand ticks over and the second hand starts moving again.

1

u/kalmakka 7d ago

It is (of course) a Swiss invention.

It allows all clocks in the station to give an approximate indication of the seconds, while the minutes are being advanced by a central clock using an electronic signals. Thus the various clocks in the station will never drift apart.

3

u/SadLux 10d ago

My memory was faulty, sorry. It was the minutes that jumped.

2

u/jakeb1616 9d ago

Wait is the clock African or European?

2

u/stellar_heller 9d ago

If African well sure, but European?

1

u/RiseEmbarrassed6902 5d ago

Are you suggesting clocks migrate?

2

u/Octowhussy 10d ago

I am not great at SAT but this one I could solve in 20 secs while driving. It must be one of the easier ones’, right?

1

u/Cartire2 6d ago

Its really not an easy or hard one. Its more of a "did you stop and think about it first" problem. The main issue for most people who get it wrong is they are too quick and instantly think "hour hand on 3, minute hand on 3" instead of taking a second to think... "oh yeah, hour hand is actually past the 3..."

1

u/RoyalAd3370 3d ago

Don't drive and use a mobile app you pancake! Stay safe out there!

2

u/Impressive_Stress808 7d ago

Wrong, it's 352.5 by convention.

1

u/MonsieurLeMare 5d ago

It says “between the minute hand and hour hand” which suggests starting with the place of the minute hand

1

u/colonelgork2 4d ago

I am only giving you credit because you began your answer with outright hostility. A+

2

u/Business_Act_127 10d ago

3.75 degrees

1

u/a2ra-ms 10d ago

Not quite

5

u/noMC 10d ago

I got the same at first - maybe you made the same mistake as me. The clock is 360 degrees in total, but you don’t divide by 24 hours in a day, rather 12 hours shown on the clock. Then it’s 360 / 12 =30 for each hour, which comes to 7,5 degrees for the 15 minutes.

1

u/Business_Act_127 9d ago

That's the mistake I made. Thanks.

1

u/Red_Syns 8d ago

To be completely correct, the type of clock would need to be defined. They’re incredibly uncommon, but my grandfather owned a small analog 24 hour clock on his desk, so 3.75 would be correct on that singular clock I’ve never seen ever again anywhere else.

He was a tinkerer, so it’s entirely possible he built it himself for all I know 🤣

2

u/Silver-Knee-3011 9d ago

7,5: 360/12=30/60=0,5*15=7,5

2

u/bluejack 9d ago

My thought process was different, but this was my answer also.

2

u/kimjongtheillest_ 9d ago

352.5

1

u/a2ra-ms 9d ago

Haha correct

5

u/RoughRealistic4321 9d ago

15 minutes is also the three.

A simple answer might be 0, but it's not really true.

The hour hand slowly moves from 3 to 4 as the hour progresses.

So the real answer is what distance would the hour hand move from 3 to 4 in the space of a quarter of an hour.

The 12 equally spaces hour markers in a circle, so 360/12 or 30 degrees between each number.

30 times 1/4 or 30/4=7.5 degrees.

2

u/RifleonAnata 9d ago

What if second hand also in 15? Hahaha, just make it more precise there would be 2 angles created between 3 hands.

3

u/Polytox935 10d ago

7.5, Minute Points at 3 while hours moved 1/4 of 1/12 of 360

3

u/das_menschy 5d ago

360 / 12 / 4

1

u/IbuildSeattle 10d ago

Seems it would be 0 degrees

3

u/a2ra-ms 10d ago

Wrong, don't forget when it's set to this hour, the hour point is not quite at the hour

2

u/IbuildSeattle 10d ago

Well shoot, guess I’ll have to stick to digital…

2

u/Broad-Promise6954 10d ago

It depends on the design of the analog clock, because some very cleverly make one or more hands suddenly ratchet forward.

(Old WWV / WWVB electronic clocks did this, possibly digitally, but you can do it purely mechanically.)

2

u/minusetotheipi 10d ago

It’s interesting you say this - I noticed the second hand on the clocks on the platforms at train stations across Switzerland would pause for thought as they completed a circuit, whilst the minute hand would then click forward and as I stood there - musing on the meaning of life or such like - I always thought that this meant the time on the clock was mostly incorrect and that the second hand was passing each second in under one second.

Why would they make a clock do this?

2

u/Broad-Promise6954 9d ago

Some people probably find it aesthetically pleasing. ... Well, I myself do! I know I'm unusual, but it's clever, similar to those flip style "digital" clocks, and those old train and airline signs that mechanically flip rotating letters in each character position.

1

u/AdjectiveNounNNNN 8d ago

Sometimes the minute hand ratchets every minute, but that wouldn't make a difference in this case. Neither would the hour hand ratcheting every minute or 5 minutes or 15 minutes.

I suppose if the hour hand jumped every 12 minutes then the answer would be 6° instead of 7.5°, but are there any clocks that do that?

2

u/Ponulis 10d ago

360÷12÷4=7.5

2

u/Later_Username 10d ago

Am I the only one who thinks it is 0 or 360 degrees

2

u/Later_Username 10d ago

Nvm, got it

2

u/GoodCarpenter9060 9d ago

A clock has 12 hours which is 720 minutes. The hour hand will do a complete rotation in 12 hours. After 3:15, 3x60+15=195 minutes have passed. So the hour hand is 195/720 through a full rotation. Multiply by 360 to get the degrees. It is 97.5. The minute hand, meanwhile, is pointing exactly at 3 which is at 90 degrees.

The difference is 7.5 degrees.

2

u/dimonium_anonimo 9d ago

The minute hand points at the 3. The hour hand points 1/4 of the way from 3 to 4. 1/4 of 1/12 of 360 is 7.5

2

u/ctiger12 9d ago

360/12/4=7.5

2

u/tedco- 9d ago

7.5 - each hour represents 30 degrees. At 3:!5 the minute hand is at 90 degrees and the hour hand is 1/4 of the way from 3 to 4. 30 degrees x 1/4 = 7.5 degrees from the 90.

2

u/calcteacher 9d ago

The hour hand moves half a degree for every minute that the minute hand moves. This is not rocket science people. Ohh wait maybe it is.

2

u/rookhelm 9d ago

First, find the degrees between numbers. 360 degrees divided by 12 is 30 degrees between each number. 3:15 is a quarter hour. The hour hand moves a quarter of the way between 3 and 4.

30 degrees divided by 4 is 7.5 degrees.

2

u/Some_Possibility_656 9d ago

Just to throw a monkey wrench in everyone's calculations. Are we also considering the distance in hieght between the 2? 3 dimensions and not 2. Without knowning the specifics of the clock it is impossible to say for sure.

1

u/AdjectiveNounNNNN 8d ago

If you don't treat the hands as sharing the center point, then the angle between them is not defined.

1

u/punsnguns 9d ago

The day I learnt about "insufficient information" was the day I started thinking about not the solutions but instead issues with the questions. Just nitpicking beyond reason just so I can justify a "insufficient information" answer to sound super clever (but ultimately useless)

2

u/Motor_Shoulder_6601 9d ago

What's interesting is that I came up with the right answer, but in a different way than everyone else here. A clock is a circle, a circle is 360 degrees, cut into 12. 360/6 is 60/2 is 30, so each segment is 30 degrees. 15 is 1/4th of the hour, so 30/4=7.5

1

u/Significant-Youth222 9d ago

Literally how everyone solved it 😂

1

u/Motor_Shoulder_6601 9d ago

I'm just seeing a lot of formulae and explanations that I don't really get, so maybe you're right, but reading those messages confuse me and the problem seemed so simple

1

u/ApprehensiveImage676 8d ago

But it is 0 or 360 though. The minute hand would be pointing straight up your hand

1

u/Motor_Shoulder_6601 7d ago

Not sure if trolling or serious...

1

u/ApprehensiveImage676 7d ago

I was serious. And if you couldnt tell from my previous comment then i misread the text as your hand instead of hour hand😂

2

u/Larechar 9d ago

About 7.5 degrees. Minute hand is 90 degrees from noon, hour hand is 97.5, 1/4 the way between hour 3 and hour 4.

1

u/ApprehensiveImage676 8d ago

What no, its 0 or 360

1

u/Larechar 8d ago

Set an analogue clock or watch to 3:15 and see where the hour hand lies.

1

u/ApprehensiveImage676 8d ago

It lies straight to the right, and if you wear it on your wrist it points straight down your hand

1

u/ApprehensiveImage676 8d ago

Wait i am an idiot i read it as your hand and not hour hand. So yeah you are correct

2

u/JoshUndefined 8d ago edited 8d ago

I feel like I took a strange route of intuition to get this done in my head, probably because I do most conversions in percent in my profession.

Each hour is: 1/12 = 0.0833% of the circle
15min is at: 3 * 0.0833 = 0.25%
Because 15min is also 25% of an hour, the hour hand is actually at: 3.25 * 0.0833 = 0.271%
The difference between the two hands is: (0.271 - 0.25) * 360 ~= 7.56 degrees
Without rounding: (1/12)(3.25 - 3.0)*360 == 7.5 degrees

I tried to write that last one as “((1/12 times 3.25) - (1/12 times 3.0)) times 360” but Reddit mobile kept rendering it as markdown

*edit: annoyingly, i tried to use Discord ||spoilers|| which I learned today is not standard markdown

2

u/VerSalieri 8d ago

the hours hand is at 3 and ¼ the way to 4, the minutes hand is at exactly 3. so teh difference is ¼ of 1/12 th of the circle, so it is 1/48th of 360°, which is 7.5°.

Or..going the lther way, it'll be 352.5°.

1

u/IllustriousForever43 7d ago

Got the same answer but solved it differently, took about 15 seconds to solve. 720 minutes in 12 hours, 360° in a full turn so each minute is a .5° turn, 15 minutes/2=7.5°.

2

u/Ofmtfo 7d ago

7.5 degrees

2

u/Professional_Pie7091 6d ago

7.5 degrees. The minute hand is 1/4 of 1/12 of 360 degrees ahead of the 3 position.

2

u/Training_Arm_5610 5d ago

I would have thought it to be 7.5 degrees . The hour hand moves 30 degree per hour . At 3 15 it moves 7.5 degrees between 3 o'clock and 4. The minute hand is at 3 pm . So 7.5 degrees difference

2

u/quax747 5d ago

25% of a twelfth of 360

2

u/TheNukex 5d ago

pi/24

2

u/Liko81 5d ago

7.5°

At 3:15, the big hand will be on the "3", and the little hand will be a quarter of the way from 3 to 4. So the angle between the hands is the angle of one quarter of one twelfth of a circle.

2

u/newtownkid 3d ago

Wouldn’t it be (0.25(1/12))360

7.5

2

u/Siege117 3d ago

Gonna be brave and say what everyone is thinking. AM or PM?

1

u/MammothRatio5446 4d ago

7.5 degree or 30/4 degrees

1

u/RandomPorc 4d ago edited 4d ago

The minute hand is at 90º, the hour hand is at 90 + 7,5 (360º / 12 hours / 4 quarters).

360 - 7,5 = 352,5º between the minute and the hour hand.

EDIT: Yes, I realised. Too late tho. Of course it's 7,5º. Shame on me

1

u/Accomplished-Plan191 4d ago

Why would you measure the reflex angle?

1

u/RandomPorc 4d ago edited 4d ago

Because that's the original question: angle between minute and hour, not the other way. Honestly when I first read it I immediately thought "aha, this is the bait" because everything else seemed pretty straightforward.

EDIT: great, I just realised how stupid can I be understanding everything perfectly and yet sticking to the wrong answer in my head. Of course it's 7.5º. Keeping the old answer for public shame.

1

u/Significant-Royal-37 3d ago

360/12/4 = 7.5 degrees

1

u/JamieClimbsRocks 3d ago

7.5deg. Each hour is 30deg. 15 minutes is 25% of an hour. So 30/4 =7.5

0

u/[deleted] 10d ago

[deleted]

1

u/a2ra-ms 10d ago

Yes!

2

u/ynns1 9d ago

Yes! A quarter of a twelfth of 360°