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Math Puzzle: Can you figure.....?
Asked by: kc5255
from PHILADELPHIA, PA
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One day an Imperial engineer was ordered by the Emperor to measure the length of a road. However, the engineer had only a single piece of rope and he did not know the exact length. What he was able to learn, however, was that if he stretched this rope out on the road 30 times, it was 2 meters too long. But if he stretched the rope out only 29 times, it was 4 meters short of the end of the road.
Can you figure out the length of both the rope and the road?
Can you figure out the length of both the rope and the road?
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(02/28/08):
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Let x = length of rope and y = length of road
It's 2 meters too long if the rope is stretched out 30 times, so 30x = y + 2
It's 4 meters too short if the rope is stretched out 29 times, so 29x = y - 4
If you multiply the second equation by -1 and then add it to the first equation, you get 30x - 29x = y + 2 - y + 4. This simplifies to x = 6.
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It's 2 meters too long if the rope is stretched out 30 times, so 30x = y + 2
It's 4 meters too short if the rope is stretched out 29 times, so 29x = y - 4
If you multiply the second equation by -1 and then add it to the first equation, you get 30x - 29x = y + 2 - y + 4. This simplifies to x = 6.
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Answer Date: 01:00am 02/28/08
Best Answer Comments from Asker: kc5255
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Thank you. A lot of you have answered correctly.. Congrats to mkay0013 who was the first to answer correctly and show their work. |
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6mts
178mts
178mts
Answer Date: 11:37pm 02/27/08
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rope is 6.66cm long and the road is 5.93m long?...
Answer Date: 12:25am 02/28/08
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rope is 6m long
road is 178m long
road is 178m long
Answer Date: 02:59am 02/28/08
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How did he know how much too long and how much too short the rope was to begin with if all he had was a piece of rope with an unknown length?
Source: Looking at the obvious.
Answer Date: 05:07pm 02/28/08
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well lets see b=length of the road, x=length of rope
29x+4=b
30x-2=b
30x - 2 = 29x +4
-29x +2 -29x +2
x=6
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29x+4=b
30x-2=b
30x - 2 = 29x +4
-29x +2 -29x +2
x=6
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Answer Date: 05:15pm 02/28/08
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x=road y=rope
If the rope is 30y=x+2
and then also 29y=x-4
y=6 simplified back into the equation
30*6-2=178
so the rope is 6 and the street is 178...
If the rope is 30y=x+2
and then also 29y=x-4
y=6 simplified back into the equation
30*6-2=178
so the rope is 6 and the street is 178...
Answer Date: 05:37pm 02/28/08
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Let length od rope be L and of road be R
29L+4 = R ... equation 1
30L - 2 = R ... equation 2
Subtracting eqaton 1 from 2 gives
L-6 = 0
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29L+4 = R ... equation 1
30L - 2 = R ... equation 2
Subtracting eqaton 1 from 2 gives
L-6 = 0
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Answer Date: 02:55am 03/03/08
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30 times is 2m too big, 29 times 4m too small therefore rope is 6m long
30 * 6 - 2 = 178m is the length of the road
30 * 6 - 2 = 178m is the length of the road
Answer Date: 03:39pm 03/03/08
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let's call the end of the road y and the rope x:
29x= y-4 and 30x=y+2
x=30x-29x
x=(y+2)-(y-4)
x=y+2-y+4
x=y-y+2+4
x=0y+6
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29x= y-4 and 30x=y+2
x=30x-29x
x=(y+2)-(y-4)
x=y+2-y+4
x=y-y+2+4
x=0y+6
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Answer Date: 03:59pm 03/04/08
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The length of the rope is six meters
Answer Date: 04:45pm 03/05/08
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