
#1
Oct1309, 03:59 PM

P: 323

If a man and a half can eat a cake and a half in a minute and a half, allowing the same situation, how many men would it take to eat 60 cakes in 30 minutes?
Btw, I'm getting these off an app on my phone. 



#2
Oct1309, 04:46 PM

P: 15,325

One cake per minute per man.
So, 2 men. I want half the prize money. 



#3
Oct1309, 07:48 PM

P: 657

If R is the number of cakes per minute that 1 man can eat, then: 1.5 men * R * 1.5 minutes = 1.5 cakes 1.5 men * R minutes = 1 cakes R = 1 cakes / (1.5 men minutes) = 2/3 cakes/men minutes Hence, we now want: Q men * 2/3 cakes/men minutes * 30 minutes = 60 cakes Q men * 2/3 = 2 men Q men = 3 men Q = 3 DaveE 



#4
Oct1309, 10:40 PM

P: 15,325

If a man and a half can eat a cake and a half in a minuteI misread. I thought it was 1,1.5,1.5 not 1.5, 1.5, 1.5. 



#5
Oct1709, 01:10 PM

P: 323

I have another one:
If you have a sphere and you remove a cylinder with a length of six inches from it (assume that the cylinder is arranged in such a way so as to go through the maximum amount of the sphere), what is the new volume? 



#6
Oct1709, 10:21 PM

P: 657

2*pi*((2/3)*R^33*R^227) (where R is the radius of the sphere.) I'm guessing that some factors are supposed to cancel out nicely? DaveE 



#7
Oct1809, 02:07 PM

P: 101

The answer is independent of radius because as the radius of the sphere increases the radius of the cylinder also increases, so the volume percentage remains the same. Kind of like why rain water depth is independent of the the volume used to measure it




#8
Oct1809, 06:46 PM

P: 657

DaveE 



#9
Oct1809, 09:06 PM

P: 101





#10
Oct1909, 05:58 AM

P: 52

What about differentiating the expression for the volume difference to find the value of radius\diameter that minimises it?
So I get for the volume difference V = 4/3*pi*(d/2)^3  6*(d^236)*pi/4 where d is the diameter of the sphere, which upon differentiating and setting to zero gives either a diameter of 9 or 15. Using 9 gives the difference as 54*pi. 



#11
Oct1909, 06:30 AM

P: 86

are we allowed complex solutions?




#12
Oct1909, 06:45 AM

P: 52

I'm not sure about complex solutions, but I just realised I factorised the quadratic wrong. I should have got a diameter of ~7.82 and a volume difference of ~43*pi.




#13
Oct1909, 07:43 AM

P: 52

Okay I've completely messed up that differentiation, I should've got d = 6 or 0 and that would maximise the volume difference so no good.




#14
Oct1909, 08:37 AM

P: 657

DaveE 



#15
Oct1909, 08:43 AM

P: 101





#16
Oct2609, 03:47 PM

P: 52

So to repeat arithmetix' question, are we allowed complex solutions? I get two possible complex ones: (45+i*9*(27)^1/2)*pi or (45i*9*(27)^1/2)*pi (assuming I haven't made anymore silly mistakes, which is a big assumption ).



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