SOLUTION: Joe need 3 days to tile a rectangular pool of even depth. How long will it take him working at the same rate to tile a pool twice as long,twice as wide and twice as deep.

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Question 581680: Joe need 3 days to tile a rectangular pool of even depth. How long will it take him working at the same rate to tile a pool twice as long,twice as wide and twice as deep.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Joe need 3 days to tile a rectangular pool of even depth. How long will it take him working at the same rate to tile a pool twice as long,twice as wide and twice as deep.
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Let original surface area be LW + 2WH + 2LH
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New surface area will be (2L)(2W) + 2(2W)(2H) + 2(2L)(2H)
= 4LW + 8WH + 8LH = 4[LW + 2WH + 2LH)
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Original time to tile = 3 days
New time to tile = 4*3 = 12 days.
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cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a = length
Let +b+ = width
Let +c+ = depth
The area to be tiled is:
+a%2Ab+ floor
+2%2Aa%2Ac+ a wall and opposite wall
+2%2Ab%2Ac+ the other wall and opposite wall
If you double each dimension, you get
+2%2Aa%2A2%2Ab+%2B+2%2A2%2Aa%2A2%2Ac++%2B+2%2A2%2Ab%2A2%2Ac+
+4%2Aa%2Ab+%2B+4%2A%282%2Aa%2Ac%29+%2B+4%2A%282%2Ab%2Ac%29+
+4%2A%28+a%2Ab+%2B+2%2Aa%2Ac+%2B+2%2Ab%2Ac+%29+
This is 4 times the area of the 1st pool, so it will take
him 4 times as long to tile it, or
3%2A4+=+12+ days