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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?
The grade indicates how much the elevation changes up or down as you walk along the street.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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?
:
With a slope that small, the horizontal dist is almost the same as the actual
distance to the river. .09 * 120 = 10.8 yds is H's house above the river
and
.09 * 360 = 32.4 yds is P's house above the river, so even if you add 7 yds
for H's house, P's house is high and dry
:
However if they want more exact value, we have to solve a couple right triangles
:
H's house is: 360-240 = 120 yds from the river
A right triangle formed by:
the horizontal dist to river
the height above the river
the distance from the river we know is 120 yds (hypotenuse)
:
9% grade, the slope rises 9 yd for every 100 yds (horizontally)
Call the horizontal distance x
then
height above the river = .09x
:
Find x using pythag:
x^2 + (.09x)^2 = 120^2
x^2 + .0081x^2 = 14400
1.0081x^2 = 14400
x^2 = 
x^2 = 14284.3
x = 
x = 119.5 yds is the horizontal distance
then
.09 * 119.5 = 10.75 yds is the height of H's house above the river
The river would have to rise 10.75 yds to flood H's basement
:
"If Hector’s house is 20 feet tall and the flood covers it completely, would
Patricia’s house suffer any flooding?
Convert 20 ft to 6.67 yds, therefore:
10.75 + 6.67 = 17.42 yd rise in the river would cover H's house.
:
How about P's house? Find her height above the river, y = horizontal dist
Same method
y^2 + (.09y)^2 = 360^2
y^2 + .0081y^2 = 129600
1.0081y^2 = 129600
y^2 = 128558.7
y = 358.55 yd is the horizontal dist
then
.09 * 358.55 = 32.27 yd above river, obviously her house is safe
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