Maths Nerds......

[Gaz #68]

its all based on the fact that the hour hand spins at a ratio of 1:12 the speed of the minute hand, so its not like the minute hand actually hits 90 degrees twice every hour.
in 24 hours the hour hand will spin twice, and the minute hand will spin a total of 24. so as it spins round it overtakes the hour hand 22 times. every time it passes it has to make 90 degrees twice in a 360 degree spin so it should be 44 right angles in total. it makes your head go fuzzy picturing it but i figured it out by sitting staring at a picture of a clock for about 10 minutes while a customer was on hold and i was pretending to be investigating a billing issue...

I stand corrected - serves me right for watching the second hand and not the minute hand on my watch I'm thinking the logic behind your explanation offers the correct solution.

 

[Liam92]

I stand corrected - serves me right for watching the second hand and not the minute hand on my watch I'm thinking the logic behind your explanation offers the correct solution.

if it makes you feel better i was sitting pointing at my screen with both my hands trying to look at where the 90 degree angles were every hour. coworkers were thinking i was going mad.

 

[leach]

Technically though, wouldnt anything past 3 oclock be over so for example if its 9 oclock it would be 270 degrees instead of 90. I would say the answer is twice per day, midnight and noon.

 

[Tom]

9 o clock would be 270, but also 90
360 degrees in a circle - 90 degrees measured one way, 270 the other

The question states right angles, not 'when is it at the 90 degree point', so a right angle is made as the hands are 90 degrees apart, not at specific points on the clock face


Lost track and made a bit of an error with midnight and noon - those are at the 0 degree point when the hands meet. They will also meet at other times

 

[leach]

was half asleep when i wrote that and in fact meant 3 pm and 3 am. my answer is definitely wrong, I just wanted to look clever

 

[ToniH]

I have one for you:

You have fresh plums which of their mass is 80% water and 4% sugars. After drying them there is only 20% water. How much sugar do dried plums consist?

 

[Liam92]

I have one for you:

You have fresh plums which of their mass is 80% water and 4% sugars. After drying them there is only 20% water. How much sugar do dried plums consist?

I want to say 16% because sugar content shouldnt reduce through drying if it is purely water content thats removed., but I'm no biologist and would expect in practise that some sugar would be lost as sugar dissolves in water?
so assuming the same volume of sugar then with less water, the proportion of sugar content increases.

 

[Cook$]

4%

 

[Tom]

4%

Can't be 4% as the sugar has remained, but the overall mass reduced
The same level of sugar is now a higher percentage of the dried mass (16%)


Fresh plum
80 water
4 sugar
16 plum
100 total

Assuming we have a fresh plum with a mass of 100

The dried plum sugar and plum components remain 4&16 but are now 80% of the mass

To identify the percentage that the 4 parts of sugar now constitute:
80%/20*4=16%

 

[ToniH]

16% was correct. That was a question from entrance exams into university to study business.

Here is another one.

We have two clocks. One runs slow 2 minutes in an hour and the other runs fast 2 minutes in an hour. They start at the same time when it is 12 o'clock. What time do they show when they next time show the same time?