Easy math puzzles
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50 members have voted
August 25th, 2025 at 10:29:43 PM
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Quote: Ace2Agree. The exact answer, which I posted on July-29, is:
[(6e^(1/6) - 7)/(e^(1/6) - 1)*(1 - 1/e^(1/6)) + 1/e^(1/6)]/(1 - 5/6*1/e^(1/6))
P.S. other people might care but aren’t capable of solving it
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Thank you! I will write up my solution in a PDF document shortly to share.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 26th, 2025 at 4:52:23 PM
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Here is my solution to the average time until the first Email or 4 rolled. It shows a simpler method that I previously described.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 27th, 2025 at 7:51:17 AM
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I may have asked this one before, but it's a classic.
It takes Alice and Bill 2 days to paint a house.
It takes Bill and Cindy 3 days to paint a house.
It takes Alice and Cindy 4 days to paint a house.
How long does it take if they all paint?
It takes Alice and Bill 2 days to paint a house.
It takes Bill and Cindy 3 days to paint a house.
It takes Alice and Cindy 4 days to paint a house.
How long does it take if they all paint?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 27th, 2025 at 8:26:03 AM
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Quote: WizardI may have asked this one before, but it's a classic.
It takes Alice and Bill 2 days to paint a house.
It takes Bill and Cindy 3 days to paint a house.
It takes Alice and Cindy 4 days to paint a house.
How long does it take if they all paint?
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Solve this by putting the problem in terms of painting rates.
Let a, b, and c be the rates for Alice, Bill, and Cindy, respectively.
a + b = 1/2, which is a rate of 0.5 house / day.
b + c = 1/3
a + c = 1/4
Sum the three equations to get: 2a + 2b + 2c = 13/12
Then: a + b + c = 13/24 houses / day
1 / (13/24 houses/day) = 24/13 days/house = 1 11/13 days, or about 1 day, 20 hours, and 18 minutes.
August 27th, 2025 at 8:41:23 AM
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Quote: ChesterDogquestions-and-answers/math/34502-easy-math-puzzles/104/#post962824]link to original post
Solve this by putting the problem in terms of painting rates.
Let a, b, and c be the rates for Alice, Bill, and Cindy, respectively.
a + b = 1/2, which is a rate of 0.5 house / day.
b + c = 1/3
a + c = 1/4
Sum the three equations to get: 2a + 2b + 2c = 13/12
Then: a + b + c = 13/24 houses / day
1 / (13/24 houses/day) = 24/13 days/house = 1 11/13 days, or about 1 day, 20 hours, and 18 minutes.
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I agree! Much simpler than how I did it.
For extra credit, how long would it take each individual person to paint the house?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 27th, 2025 at 10:00:17 AM
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Quote: WizardQuote: ChesterDogquestions-and-answers/math/34502-easy-math-puzzles/104/#post962824]link to original post
Solve this by putting the problem in terms of painting rates.
Let a, b, and c be the rates for Alice, Bill, and Cindy, respectively.
a + b = 1/2, which is a rate of 0.5 house / day.
b + c = 1/3
a + c = 1/4
Sum the three equations to get: 2a + 2b + 2c = 13/12
Then: a + b + c = 13/24 houses / day
1 / (13/24 houses/day) = 24/13 days/house = 1 11/13 days, or about 1 day, 20 hours, and 18 minutes.
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I agree! Much simpler than how I did it.
For extra credit, how long would it take each individual person to paint the house?
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1) a + b = 1/2
2) b + c = 1/3
3) a + c = 1/4
Subtracting 2) from 1) yields:
4) a - c = 1/6
Adding 3) and 4) yields:
2a = 5/12
a = 5/24 houses/day
1 / (5/24 houses/day) = 24/5 days/house = 4.8 days for Alice to paint a house, which is 4 days, 19 hours, and 12 minutes.
b = 1/2 - a = 1/2 - 5/24 = 7/24 houses/day
1 / (7/24 houses/day) = 24/7 days/house = 3 3/7 days for Bill to paint a house, which is about 3 days, 10 hours, and 17 minutes.
c = 1/4 - a = 1/4 - 5/24 = 1/24 houses/day
1 / (1/24 houses/day) = 24 days for Cindy to paint a house
