The worlds first riddle!

[size=8]$370.37[/size]

Don't you got no work to do?

Here am I standing by this here tank, I don't know the size, and I can't go home till it's filled.


One pipe can fill a water tank in 50 minutes. Another pipe can fill the same water tank in 40 minutes. How much time would it take if both pipes were to fill the same water tank at the same time

22 2/9 min

markr,

markr's answer looks right, i was looking at my notes for solving this problem ...i did things a bit differently, and i know my solution worked because i wrote a cool program with it, but i can't figure out what i was thinking. apologies.

Use each digit from 1-9 once:

Mark:

CHICKEN
1 egg per chicken each 1.5 weeks.
4 eggs in 6 weeks


The common mistake is to reduce all three quantities to 1 (1 chicken. 1 egg, 1 week). However, if you think carefully about it, this is not the case. For example, imagine you have 8 painters in your 8 room house and they finish in 8 hours. Would this mean 1 painter could paint 1 room in 1 hour? Heck no. 1 painter can paint one room in EIGHT HOURS. Returning to the puzzle, we then can say that 1 chicken could lay one egg in a WEEK AND A HALF. Therefore, Mark has it right.




NO REMAINDER
2^3 * 3^2 * 5 * 7 = 2520



This number would have to have as its factors 1, 2, 3, 4, 5, etc. Since any number has 1 as a factor, we can eliminate it. We will need the 2 and 3. Now, when we get to 4, we already have 2 as a factor so we just need another 2. 5 is prime so we will need that. We already have 6 as a factor because 2 x 3 = 6. 7 is prime and so we will need that. We do not need 8 as a factor because it is 2x2x2 and since we already have a '4', we just need another 2. Since we already have a 3, we just need another 3 to make a '9'.We do not need the 10 because 2x5 = 10. Therefore, to put it another way, our number is: 2 x 3 x 2 x 5 x 7 x 2 x 3 = 2,520.
Which as you can see, is remarkably similar to the one Mark posted.




$250 bonus

370.37



Adding the 3 tax rates together gives us a total tax rate of 32.5%.
1)Tax = Gross Pay * .325
2)Gross Pay - Tax = Net Pay
Substituting Equation 1 into 2 produces:
Gross Pay -.325*Gross Pay =Net Pay. Since we are looking for $250 Net Pay
then Gross Pay -.325*Gross Pay = $250
.675 * Gross Pay = $250
Gross Pay = 370.37




Thoh:

PIPES

22 2/9 min





There is a formula for this type of problem but just by using logic, the answer is easily obtained. Assume the tank is 50 gallons. So the 'slow' pipe can fill it up at a rate of 1 gallon per minute. The 'fast' pipe can fill it up at a rate of1.25 gallons per minute. Therefore, with both pipes working together, the tank is filling at a rate of 2.25 gallons per minute. Since it is a 50 gallon tank, then it will fill up in (50/2.25) minutes or 22 minutes and 13 and a third seconds.

If you want to use the formula, it is (Rate1 x Rate2)/(Rate1 + Rate2) = Time.




Stu wrote, "I can't figure out what I was thinking."

Congratulations, you have passed the entry criteria necessary to join our club.




Talking about angles is this the world's shortest question:

A triangle has sides of 50, 70 and 80. What are its angles




In an effort to ensure Mark's puzzle does not get lost, I repeat it again. Should it not reproduce correctly, do check it out above, it is a good one.


Use each digit from 1-9 once:

[size=8]TRIANGLE
38.21, 60, 81.79 (law of cosines)[/size]

markr's puzzle:
[size=7]17*4 = 68
68+25 = 93[/size]

stuh505 provided the correct answer to the digit problem.

Damn, I mean, well done. Please don't type the answer, I still can't get it.

While you wait for me to catch up…


If a rubber ball is dropped from the Leaning Tower of Pisa at a height of 90 meters from the ground, and on each bounce the ball rises exactly one-tenth of its previous height, what distance will it travel before it comes to rest



A man wears a clean shirt every day. If he drops off his laundry and picks up the previous week's load every Tuesday night, how many shirts must he own to keep him going



Use all the numbers 1 2 3 4 5 6 7 8 9 in that order.
Insert +, -, *, and / or parentheses between the numbers to find a total of 30

ball: 110 meters
shirts: 15
#s: 1(2+3)4/5*6+7+8-9

[size=8]((12-(3x4))x5)+6+7+8+9[/size]

Mark:


TRIANGLE
38.21, 60, 81.79 (law of cosines)



(Law of the Jungle)

Draw a triangle diagram so that the 50 is on the left, 70 is on the right and the base is 80. Now draw a perpendicular to the base. This perpendicular will have a height 'h' another side 'x' and a hypotenuse of 50.


From the Pythagorean Theorem, 502 =h2 plus x2.
The triangle on the right has height 'h' a side of (80-x) and a hypotenuse of 70. Again using the Pythagorean Theorem, 702 =h2 plus (80-x)2.
Since h2 appears in both equations, we obtain an equation of:
2,500 - x2 = 702-(80-x)2

This reduces to x equalling 25. By substitution, we obtain h=43.30127019. From trigonometry we look up the arctangent of (h/x) = arctan (1.732050808) which equals 60 degrees exactly. The angle at the other side of the base equals arctanm (43.30127019/55) or 38.2132107 degrees. Since all triangles have 180 degrees, the 3rd angle is calculated to be 81.7867893.



Thoh:

ball: 110 meters


90+9u+9d+.9u+.9d+....=110m


shirts: 15




Numbers = 30

Thoh: #s: 1(2+3)4/5*6+7+8-9

Mark: ((12-(3x4))x5)+6+7+8+9

Me: (1+2)*3+4+5+6+7+8-9=30

I thought mine was a unique solution!

Which probably accounts for the fact that I was unable to come up with a solution to your problem Mark. Is it unique, or there other combinations out there?


Ever wonder how a mountain's height is determined, especially when a tape measure cannot be brought to the peak nor can it be brought to the inside of the base of the mountain?

Well, here is one way to do it (assume we are working on level ground and using a transit exactly 5 feet off of the ground). From a certain distance, the mountain peak has an angular elevation of 40 degrees. Moving precisely 1,000 feet closer to the mountain, its angular elevation is now 42 degrees.

What is the height of the mountain

It's unique.

height = 5 + 1000/[(tan(42*)/(tan(40*)-1] which is approximately 13692.4 feet

"It's unique"

Thank you, it was good.



Mountain
Woops, that is not the number I have. If others pass this way and support it, I am in trouble. Time to get the tape out I think.

thoh is on the right track but made a mistake

H-5 = height of mountain
D = original distance from mtn

tan(40) = H/D
tan(42) = H/(D-1000)

H/tan(40) = H/tan(42)+1000

H(1/tan(40) - 1/tan(42)) = 1000

height = 1000/(1/tan(40) - 1/tan(42)) + 5 = 12329.2 ft

looks like thoth tried to simplify by multuply by tan(42), but forgot to multiply the right side, which is why it is off by 10%

I agree with stuh505, although not before banging my head against the wall thinking that 40 and 42 represented the sight angles from the base to the peak (no right triangles). I resorted to an iterative solution using Excel. After seeing that my answer differed from stuh505's (and didn't match his explanation), I reread the problem. It's a bit easier than what I was trying to solve.

What is the height of the mountain?

Stuh:

H-5 = height of mountain
D = original distance from mtn

tan(40) = H/D
tan(42) = H/(D-1000)

H/tan(40) = H/tan(42)+1000

H(1/tan(40) - 1/tan(42)) = 1000

height = 1000/(1/tan(40) - 1/tan(42)) + 5 = 12329.2 ft

Nice, clean and totally correct.

Close Thoh, and all in half a line.
Mark. I have noticed that you often use Excel to come up with some remarkable answers, does Microsoft know the uses to which it is put?



For the record:
The distance from the 2nd measurement will be called 'x'. The distance from the 1st measurement is therefore '1000 plus x'. We now form the two equations:

1) tan 40 = h/(1000 + x) OR h=tan 40 * (1000 + x)
2) tan 42 = h/x OR h=tan42 * x

Where 'h' is the height of the mountain.

Since h is equal to both equations then, tan 40(1000 + x) = tan 42 * x
This becomes:
839.0996312 + .839099631 * x =.900404044 * x 839.0996312 = .061304413 * x
Therefore x = 13,687.4 feet
tan 42 = h/x
h = .900404044 * 13,687.4
Height of mountain = 12,324.2 feet plus 5 foot transit height:
Height = 12,329.2 feet.
Height = 5 + 1000/[(tan(42*)/(tan(40*)-1] which is approximately 13692.4 feet




Before I finally get to turn in, may I leave you with an outta this world problem.


When the Sun, Earth and Mars 'line up' (in that order), Mars is said to be in 'opposition'. The Earth takes 365.25 days to orbit the Sun and Mars takes 687.0 days.

How much time elapses from one such opposition to the next
(In days if you please, not decades)

[size=8]OPPOSITION
Assuming circular orbits, 779.88 days.

T/687 + 1 = T/365.25[/size]