document.write( "Question 329017: Patricia lives in a house on a hill. The grade of her street is 9%. The street ends at a river bank 360 yards from her front door. Hector, Patricia’s boyfriend, lives in a house 240 yards down from hers. How much does the river level have to rise about the river bank to flood Hector’s basement? If Hector’s house is 20 feet tall and the flood covers it completely, would Patricia’s house suffer any flooding?\r
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\n" ); document.write( "The grade indicates how much the elevation changes up or down as you walk along the street.
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Algebra.Com's Answer #235950 by ankor@dixie-net.com(22740)\"\" \"About 
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Patricia lives in a house on a hill. The grade of her street is 9%.
\n" ); document.write( " The street ends at a river bank 360 yards from her front door.
\n" ); document.write( " Hector, Patricia’s boyfriend, lives in a house 240 yards down from hers.
\n" ); document.write( " How much does the river level have to rise about the river bank to flood Hector’s basement?
\n" ); document.write( " If Hector’s house is 20 feet tall and the flood covers it completely, would
\n" ); document.write( "Patricia’s house suffer any flooding?
\n" ); document.write( ":
\n" ); document.write( "With a slope that small, the horizontal dist is almost the same as the actual
\n" ); document.write( " distance to the river. .09 * 120 = 10.8 yds is H's house above the river
\n" ); document.write( "and
\n" ); document.write( ".09 * 360 = 32.4 yds is P's house above the river, so even if you add 7 yds
\n" ); document.write( "for H's house, P's house is high and dry
\n" ); document.write( ":
\n" ); document.write( "However if they want more exact value, we have to solve a couple right triangles
\n" ); document.write( ":
\n" ); document.write( "H's house is: 360-240 = 120 yds from the river
\n" ); document.write( "A right triangle formed by:
\n" ); document.write( " the horizontal dist to river
\n" ); document.write( " the height above the river
\n" ); document.write( " the distance from the river we know is 120 yds (hypotenuse)
\n" ); document.write( ":
\n" ); document.write( "9% grade, the slope rises 9 yd for every 100 yds (horizontally)
\n" ); document.write( "Call the horizontal distance x
\n" ); document.write( "then
\n" ); document.write( "height above the river = .09x
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\n" ); document.write( "Find x using pythag:
\n" ); document.write( "x^2 + (.09x)^2 = 120^2
\n" ); document.write( "x^2 + .0081x^2 = 14400
\n" ); document.write( "1.0081x^2 = 14400
\n" ); document.write( "x^2 = \"14400%2F1.0081\"
\n" ); document.write( "x^2 = 14284.3
\n" ); document.write( "x = \"sqrt%2814284.3%29\"
\n" ); document.write( "x = 119.5 yds is the horizontal distance
\n" ); document.write( "then
\n" ); document.write( ".09 * 119.5 = 10.75 yds is the height of H's house above the river
\n" ); document.write( "The river would have to rise 10.75 yds to flood H's basement
\n" ); document.write( ":
\n" ); document.write( "\"If Hector’s house is 20 feet tall and the flood covers it completely, would
\n" ); document.write( "Patricia’s house suffer any flooding?
\n" ); document.write( "Convert 20 ft to 6.67 yds, therefore:
\n" ); document.write( "10.75 + 6.67 = 17.42 yd rise in the river would cover H's house.
\n" ); document.write( ":
\n" ); document.write( "How about P's house? Find her height above the river, y = horizontal dist
\n" ); document.write( "Same method
\n" ); document.write( "y^2 + (.09y)^2 = 360^2
\n" ); document.write( "y^2 + .0081y^2 = 129600
\n" ); document.write( "1.0081y^2 = 129600
\n" ); document.write( "y^2 = 128558.7
\n" ); document.write( "y = 358.55 yd is the horizontal dist
\n" ); document.write( "then
\n" ); document.write( ".09 * 358.55 = 32.27 yd above river, obviously her house is safe \n" ); document.write( "
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