Math Fun
#1144829
03/15/18 03:24 PM
03/15/18 03:24 PM
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Joined: Aug 2000
Posts: 52,993 Upstate NY
Pandora
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Sonic Boomer
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OP
Sonic Boomer
Joined: Aug 2000
Posts: 52,993
Upstate NY
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Here are a few toughies! Don't forget to show your work. -1. Isaac and Albert wanted to take a vacation. They were debating how they could get to their hotel in the fastest manner. Isaac said, "We should go by train." But Albert said, "No, the train reaches the end of the line half way to the hotel -- we would have to walk the rest of the way. We should bike to the hotel instead." Isaac disagreed. So Albert biked the whole way to the hotel, while Isaac took the train for the first half of the journey and walked for the remainder. The speed of the train turned out to be four times that of the bike's speed. The bike's speed turned out to be two times faster than walking speed. Who got to the hotel first? -2. You're a cook in a restaurant in a quaint country where clocks are outlawed. You have a four minute hourglass, a seven minute hourglass, and a pot of boiling water. A regular customer orders a nine-minute egg, and you know this person to be extremely picky and will not like it if you overcook or undercook the egg, even by a few seconds. What is the least amount of time it will take to prepare the egg, and how will you do it? -3. Two alligator breeders were talking one day, and in the course of their conversation they noticed a curious coincidence. If alligator breeder #1 were to sell alligator breeder #2 seven alligators, then breeder #1 would have exactly as many alligators as breeder #2. On the other hand, if alligator breeder #2 were to sell alligator breeder #1 seven alligators, then breeder #1 would have exactly twice as many alligators as breeder #2. How many alligators did each breeder have? -4. A drove of sheep and chickens have a total of 99 heads and feet. There are twice as many chickens as sheep. How many of each are there? -5. An eccentric individual makes it is life's work to tie a rope around the earth's equator. He buys a lot of rope and makes the attempt. A rival of his, not to be outdone, decides he wants to tie a rope around the earth's equator that is elevated from the ground by one yard at all points along the rope. How much more rope does he need? Assume the earth is perfectly spherical.
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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Re: Math Fun
[Re: Pandora]
#1144864
03/15/18 05:16 PM
03/15/18 05:16 PM
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Joined: Jul 2002
Posts: 29,148 Unionville
manxman
Sonic Boomer
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Sonic Boomer
Joined: Jul 2002
Posts: 29,148
Unionville
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4. 9 sheep and 18 chickens let x be the number of sheep. Then 2x will be the number of chickens. sheep 4 feet plus 1 head. chicken 2 feet plus 1 head. 5x+3(2x)=99 Therefore 11x=99 and x=9
Last edited by manxman; 03/15/18 05:26 PM. Reason: showed work
Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
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Re: Math Fun
[Re: Pandora]
#1144867
03/15/18 05:29 PM
03/15/18 05:29 PM
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Joined: Nov 2004
Posts: 21,908 Bucks, England
Urban Worrier
True Blue Boomer
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True Blue Boomer
Joined: Nov 2004
Posts: 21,908
Bucks, England
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5. Length of rope around equator = 2*pi*r Length of rope 1 yard above equator = 2*pi*(r+1) Extra rope needed = 2*pi*(r+1) - 2*pi*r = 2*pi yards, just short of 19 feet. Amazing
To waste one second of one's life is a betrayal of one's self. I wonder what's on television...?
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Re: Math Fun
[Re: Pandora]
#1144887
03/15/18 08:10 PM
03/15/18 08:10 PM
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Joined: Aug 2000
Posts: 52,993 Upstate NY
Pandora
OP
Sonic Boomer
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OP
Sonic Boomer
Joined: Aug 2000
Posts: 52,993
Upstate NY
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I think you're in for a sleepless night, Rog. Because I'm all heart, here's a clue: a(b+c) = ab + ac
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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Re: Math Fun
[Re: Pandora]
#1144899
03/15/18 10:51 PM
03/15/18 10:51 PM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
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Posts: 18,719
Ottawa Ontario Canada
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x = breeder#1, y = breeder#2
"If alligator breeder #1 were to sell alligator breeder #2 seven alligators, then breeder #1 would have exactly as many alligators as breeder #2."
x - 7 = y + 7 x = y + 14 [1]
"If alligator breeder #2 were to sell alligator breeder #1 seven alligators, then breeder #1 would have exactly twice as many alligators as breeder #2."
x + 7 = 2(y - 7) x + 7 = 2y - 14 x = 2y - 21 [2]
[1][2]: 2y - 21 = y + 14 2y - y = 14 + 21 y = 35 ; from [1]: x = 35 + 14 = 49
I'm a man of few words, BUT I use 'em often!!
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Re: Math Fun
[Re: Pandora]
#1144925
03/16/18 07:14 AM
03/16/18 07:14 AM
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Joined: Nov 2004
Posts: 21,908 Bucks, England
Urban Worrier
True Blue Boomer
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True Blue Boomer
Joined: Nov 2004
Posts: 21,908
Bucks, England
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Someone put me out of my misery, puhleeze! Assuming my initial statements are correct, extra rope needed = 2*pi*(r+1) - 2*pi*r Expanding, using Sue's hint, extra rope needed = 2*pi*r + 2*pi*1 - 2*p1*r = 2*pi*1 = 2*pi = 6.284 yards
To waste one second of one's life is a betrayal of one's self. I wonder what's on television...?
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Re: Math Fun
[Re: Pandora]
#1144942
03/16/18 09:31 AM
03/16/18 09:31 AM
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Joined: Aug 2000
Posts: 52,993 Upstate NY
Pandora
OP
Sonic Boomer
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OP
Sonic Boomer
Joined: Aug 2000
Posts: 52,993
Upstate NY
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Oh wait, I'm the one who needs the math lesson!! 19 feet IS a bit over 6 yards (the correct answer). Rog, why did you answer in feet? Denis, CCb, and Rog, great solves!
The moon is actually more useful than the sun since the moon gives us light at night when it's dark. The sun only gives us light during the day when it's already bright out.
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Re: Math Fun
[Re: Pandora]
#1144963
03/16/18 10:45 AM
03/16/18 10:45 AM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
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"The speed of the train turned out to be four times that of the bike's speed." "The bike's speed turned out to be two times faster than walking speed." .................................................................................................
2d = total distance, b = bike speed So train speed = 4b, walk speed = b/2
Since time = distance / speed:
Time by Albert using bike: 2d / b [1]
Time by Isaac: d / (4b) + d / (b/2) = 2.25d / b [2]
Since [1]'s numerator is lesser than [2]'s numerator, and both have the same denominator, then Albert gets there first, and has a beer waiting for Isaac!
I'm a man of few words, BUT I use 'em often!!
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