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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Why did the vector cross the road?

It wanted to be normal.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Well done, mathsyperson!

Problem # k + 94

If 1/a + 1/b + 1/c = 1/(a+b+c); a+b+c≠0 and abc≠0, what is the value of (a+b)(b+c)(c+a)?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

Nice job, Mathsyperson! I spent like twenty minutes to come up with the same answer using the disk method of integration.

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

This is not my type of problem, but here goes nothing.

*edit

Duh! I forgot to subtract abc from **both** sides of the equation.

*Last edited by irspow (2006-02-19 01:14:16)*

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

irspow, please check the solution you posted again

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 95

1 man or 2 women or three boys can do a work in 55 days. In how many days can 1 man, 1 woman and 1 boy do the same work?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

So a=-c or a=-b and

*Last edited by krassi_holmz (2006-02-18 22:26:54)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

k+95:

1m-1/55 per day

1w-1/110 per day

1b-1/165 per day

t-the numbers of days:

t(1/55+1/110+1/165) = 1;

t(1/30)=1;

t=30 days.

IPBLE: Increasing Performance By Lowering Expectations.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Yeah

IPBLE: Increasing Performance By Lowering Expectations.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 96

Can a majority of the numbers from 1 to a million be represented as the sum of a square and a (non-negative) cube?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I don't know if it was appropriate to say QED in that, but it's just really cool to say. ^_^

Why did the vector cross the road?

It wanted to be normal.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

mathsyperson, you are correct!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

By mathimatical law, you can only say QED when you start out with "Pf" or "Proof". But we'll let you go with a warning this time.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 97

Two men set out at the same time to walk towards

each other from points A and B, 72 km apart. The first man

walks at the constant rate of 4 km/hr. The second man walks

1 km the first hour, 2 km the second hour, 3 km the third hour

and so on. When will the two men meet?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Why did the vector cross the road?

It wanted to be normal.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

On k + 89, I meant to multiply by 3, but then I still would be wrong.

I wish there was a theorum to get the number that is close to this 3.

I'll have to work on that. The 3 multiplier would be like having 4 + 4 + 4 in the numerator.

I know it is wrong, but I feel the need to research this further.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

On k + 89, I was below with this 3 times correction still by factor of 1.062801932.

So with the new correction factor, it's kind of dumb, but, you'll laugh, but...

percentage that it was from machine B knowing first that the piece is

defective = 35% ((4 x 3)/(5 + 4 + 2)) * correction factor, where correction factor = (5 + 4 + 2)/(3*(.35 x 4 + .25 x 5 + .40 x 2))

**igloo** **myrtilles** **fourmis**

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

*Last edited by irspow (2006-02-20 16:00:28)*

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Solution to Problem # k + 97

After 8 hours, the first man has walked (8x4) kilometers, i.e. 32 kilometers.

After 8 hours, the second man has walked (1+2+3+4+5+6+7+8) kilometers, i.e. 36 kilometers. In the ninth hour, the first man is walking at 4 km/hr and the second is walking at 9 km/hr. Let them meet after time t hours.

Hence, 4t+9t=4, 13t=4, t=4/13 hours = 18.46 minutes approximately.

Hence, they would meet after 8 hours and 18.46 minutes approximately.

mathsyperson is correct

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

Problem # k + 98

A and B are two stations 300 km apart. Two trains T1

and T2 start from A and B respectively, towards each other at

the same time. T1 reaches B nine hours and T2 reaches A four

hours after they meet. Find the difference between the speeds

of T1 and T2.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

lol. You love this instantaneous velocity. I stand by my k+97 solution(s). There was nothing in the question that required the solution agreed upon. Distance travelled does not prove constant velocity during a time period. I have yet to see an instance of infinite acceleration either. My equations describe the motion of both people as correctly as your assumptions.

I am not trying to dispute your solution, just pointing out that the wording of a problem is just as vitally important as the mathematics that lead to a solution. Your solution **and** mine are equally valid given the way in which it was worded. More details would be needed to invalidate either one.

My answers are more correct though! Just kidding. Why quibble over less than 30 seconds?

*Last edited by irspow (2006-02-21 03:42:33)*

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 43,550

I concede you're correct too, irspow! The time given to solve the problem was about a minute! I thought the best way to do that was the way I solved

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 1,055

Thanks for the concession. lol. Interesting how **both** are correct and yet different with a problem stated as such, no?

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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