Here are some Simple Maths Problems.... First to solve them wins....

Post your answers!!!...

1. (As posted in Beethoven's Cafe) A train is traveling at 90 kilometers an hour, it is 100 meters long, and is about to go through a 400 meter long tunnel. How long will the train take to completely pass through (Including the last carriage)?

2. It is the month of June, this particular year, June has 5 Saturdays, and 5 Sundays... What will be the day on the 10th?

3. A man wishes to sell a puppy for $11. A customer wants to buy it but only has foreign currency. The exchange rate for the foreign currency is 11 round coins = $15, 11 square coins = $16, 11 triangular coins = $17. How many of each coinage should the customer pay?

Have a go!!!

Best Regards,
Luke.

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- Luke.

1. 20s
2. monday
3. 7 round + 1 square

Whatever he said....

11:18:07 - 7:30:03 = 3:48:04

= very slow going!


BTW: Did you win the quiz with that?

(A new Boinc project perhaps: Distributed quiz solving?...)

:-p

Cheers,
Martin

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See new freedom: Mageia Linux
Take a look for yourself: Linux Format
The Future is what We all make IT (GPLv3)

It was after 10:00 BST that I came to the cafe. Some of us have work to do, and I had delayed my break because my workmates were all supposed to leave for an industry show and conference (read drink lots of beer and ogle young ladies) at 9:00, they were only 58mins late in leaving. They blamed the boss.

Have I won, don't know, are my answers right?

It's now afternoon tea break, a little early.

edit] I only cam to cafe to look for music, Ipod battery is dead I think. Found some take 5 and unsquare dance by dave brubeck 1961, memories of school days.

"Take Five" by Dave Brubeck was popular in late 1961 in both the United Kingdom and the US. However, "Unsquare Dance" by him was popular in January 1962 in the US and June 1962 in the UK. References: "Billboard/RecordResearch" and "EveryHit.com".

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WinterKnight wins!!!....
3 out of 3....

Answers:
1. 20 seconds
2. Monday
3. 7 Circular Coins, 1 Square Coin

Here are some more....

4. A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on a lathe, and 20 minutes of sanding to be completed. A chair sells for $10 and a table sells for $20. How many tables and chairs should the factory produce per hour to yield the highest revenue, and what is that revenue?

5. An airplane weighs 10,000 pounds, has a 1000 gallon tank, burns fuel at a rate of 5 gallons per minute, and has a speed in miles per hour of 6,000,000 divided by the sum of weight of the plane and remaining fuel. Each gallon of fuel weighs 10 pounds. With a full tank how far can the plane fly?

6. It is your task to deliver as much grain as possible from city A to city B. The cities are 1,000 miles apart. You initially have 10,000 pounds of grain. Your camel may carry up to 1,000 pounds and eats 1 pound of grain per mile traveled. You may leave grain along the way and return to it later. How much grain can you deliver to city B?

Number two is going to be the hardest...

Post Your Answers....

Best Regards,
Luke

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- Luke.

Thank you,
I will let someone else take the credit with the next questions.

Quick look, and I'm just up and on first coffee of the day, says questions 5 & 6 are easy enough to do in head and q4 needs pencil and paper.

Here are the current standings:

1. WinterKnight - 3 Questions
2. TBD...

Have a go everyone on Questions 4,5,6... which are posted above...

Best Regards,
Luke.

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- Luke.

WinterKnight wins!!!....
3 out of 3....

Answers:
1. 20 seconds
2. Monday
3. 7 Circular Coins, 1 Square Coin

Here are some more....

4. A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on a lathe, and 20 minutes of sanding to be completed. A chair sells for $10 and a table sells for $20. How many tables and chairs should the factory produce per hour to yield the highest revenue, and what is that revenue?

5. An airplane weighs 10,000 pounds, has a 1000 gallon tank, burns fuel at a rate of 5 gallons per minute, and has a speed in miles per hour of 6,000,000 divided by the sum of weight of the plane and remaining fuel. Each gallon of fuel weighs 10 pounds. With a full tank how far can the plane fly?

6. It is your task to deliver as much grain as possible from city A to city B. The cities are 1,000 miles apart. You initially have 10,000 pounds of grain. Your camel may carry up to 1,000 pounds and eats 1 pound of grain per mile traveled. You may leave grain along the way and return to it later. How much grain can you deliver to city B?

Number two is going to be the hardest...

Post Your Answers....

Best Regards,
Luke

Anyone got any answers???

Luke.

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- Luke.

Actually #2 looks the easiest... straightforward integral. The other two look tedious. :^p

An airplane weighs 10,000 pounds, has a 1000 gallon tank, burns fuel at a rate of 5 gallons per minute, and has a speed in miles per hour of 6,000,000 divided by the sum of weight of the plane and remaining fuel. Each gallon of fuel weighs 10 pounds. With a full tank how far can the plane fly?

5 gals./min. fixed consumption rate is 1000/5 = 200 mins. flying time. Divide 6,000,000 by 60 = 100,000 for miles per minute.

V = 100,000 / ( 10,000 + (10,000 - 50T))
  = 100,000 / ( 20,000 - 50T )
  = 2,000 / 400 - T

When velocity is integrated over time, distance is the area under the curve, so


	200
	/
D =	| (2,000 / (400 - T)) dT
	/
	0
		
		200
		/
 =	2,000	| (1 / (400 - T)) dT
		/
		0
		
Integral of 1/(ax+b)dx is (1/a)(ln |ax+b|), so:

D = 2,000 ((1/-1) ln (|(-T + 400|)
	= (2,000 * -1 * ln|-200 + 400|) - (120,000 * -1 * ln|-0 + 400|)
	= 1386.2943611198906188344642429164
	~	1386.29 miles

Miles? Gallons? Must be some made-up units to make the question more abstract. ;^)

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Congratulations, Mr. Kevvy!!!!

Question 4 Answer: 1,386.29 Miles

Current Standings:

1. WinterKnight - 3 Correct Questions
2. Mr. Kevvy - 1 Correct Question
3. TBD...

two questions Remain, can anyone snap them up? Here they are....

4. A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on a lathe, and 20 minutes of sanding to be completed. A chair sells for $10 and a table sells for $20. How many tables and chairs should the factory produce per hour to yield the highest revenue, and what is that revenue?

6. It is your task to deliver as much grain as possible from city A to city B. The cities are 1,000 miles apart. You initially have 10,000 pounds of grain. Your camel may carry up to 1,000 pounds and eats 1 pound of grain per mile traveled. You may leave grain along the way and return to it later. How much grain can you deliver to city B?

Luke.

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- Luke.

Congratulations, Mr. Kevvy!!!!

Question 4 Answer: 1,386.29 Miles

Current Standings:

1. WinterKnight - 3 Correct Questions
2. Mr. Kevvy - 1 Correct Question
3. TBD...

two questions Remain, can anyone snap them up? Here they are....

4. A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on a lathe, and 20 minutes of sanding to be completed. A chair sells for $10 and a table sells for $20. How many tables and chairs should the factory produce per hour to yield the highest revenue, and what is that revenue?

6. It is your task to deliver as much grain as possible from city A to city B. The cities are 1,000 miles apart. You initially have 10,000 pounds of grain. Your camel may carry up to 1,000 pounds and eats 1 pound of grain per mile traveled. You may leave grain along the way and return to it later. How much grain can you deliver to city B?

Luke.

Here are some hints for youse guys.


In fact, does the grain reside initially in city A? Can the Camel travel in a straight and level path ? Does the camel eat the grain in his load or can he find grain along the way? Appears to be an incompletely specified problem. Assumptions will be made therefore.

The camel could move 333 pounds 333 miles on one round trip and consume the rest of the thousand pound load himself. On the tenth such trip he could deliver 666 pounds since he wouldn't have to go back. So there would be 10 times 333 and one extra 333 at the 333 mile marker or 3663 pounds. Another such excursion would move only 999 +333 lbs to the 666 mile marker or 999 (1000 actually) + 333.

So we now have 1333 lbs at the 666 mile marker. We could then get 666 lbs to the city B location-it would not make sense to go back at that point for the rest of the grain. So there is one solution-are there any others. Can calculus show whether this is optimal.

I will give everyone a hint on number 4. It is a rather simple Linear Programming problem.

Write the equations for the resource usage for a table and a chair, write the equations for the constraints (i.e. cannot exceed the resource capacity of the machines per hour.)

Then write the objective functon (maximize revenue given by X number of tables times $20 and Y number of chairs times $10)

You could then use the Simplex method for solving equations with three unknowns or find the Dual of the problem in 2 dimensions and solve it graphically.

"You see it's elementary my dear Watson."

How about some comments on my camel solution. Can anyone find a better solution? I have no proof that mine is optimal.

Since there have been no posts following up on my hints, I will give my answer to the furniture problem. It is to make all tables at the rate of 54 per hour at an hourly gross revenue of $1080. I last took an Operations Research course 40 years ago so I hope that the rust hasn't caused me to come up with the wrong, optimal answer.

Challenge you all to find a better solution. Is Karmarkar still around ??

regards,

Bill
AKA DADDIO

How about some comments on my camel solution. Can anyone find a better solution? I have no proof that mine is optimal.

Since there have been no posts following up on my hints, I will give my answer to the furniture problem. It is to make all tables at the rate of 54 per hour at an hourly gross revenue of $1080. I last took an Operations Research course 40 years ago so I hope that the rust hasn't caused me to come up with the wrong, optimal answer.

Challenge you all to find a better solution. Is Karmarkar still around ??

regards,

Bill
AKA DADDIO

Just looked at my scribbles from the other day, I made it 48 tables and 24 chairs, thats $1200.

Congratulations WinterKnight!!
You've correctly answered Question 4.

Answer: 48 Tables, 24 Chairs. Profit $1200

Current Stats....

1. WinterKnight - 4 Correct Questions
2. Mr. Kevvy - 1 Correct Question


One old unanswered question remains... Number 6

6. It is your task to deliver as much grain as possible from city A to city B. The cities are 1,000 miles apart. You initially have 10,000 pounds of grain. Your camel may carry up to 1,000 pounds and eats 1 pound of grain per mile traveled. You may leave grain along the way and return to it later. How much grain can you deliver to city B?

After this is solved, I will post three more... can anyone catch WinterKnight?

Best Regards,
Luke.

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- Luke.

Congratulations WinterKnight!!
You've correctly answered Question 4.

Answer: 48 Tables, 24 Chairs. Profit $1200

Current Stats....

1. WinterKnight - 4 Correct Questions
2. Mr. Kevvy - 1 Correct Question


One old unanswered question remains... Number 6

6. It is your task to deliver as much grain as possible from city A to city B. The cities are 1,000 miles apart. You initially have 10,000 pounds of grain. Your camel may carry up to 1,000 pounds and eats 1 pound of grain per mile traveled. You may leave grain along the way and return to it later. How much grain can you deliver to city B?

After this is solved, I will post three more... can anyone catch WinterKnight?

Best Regards,
Luke.

Yikes: you are correct I wrote down $5 per chair in my objective function !! Blame it on the glasses !!

Nice going

Well you would be correct if that was the original question.....
One Last Question Remains...

For that question, see my post above...

Luke.

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- Luke.

The answer to Q6 is: not a lot.

Lol. Can you define "not a lot" to a number answer, with 2 decimal places?

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- Luke.