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Question 102857: Show a complete solution to each problem.
Word Problem#1
Big plane. At full throttle a light plane flies 275 miles against the wind in the same time it flies 325 miles with the wind. If the plain flies at 120 mph at full throttle in still air, then what is the wind speed?
Word Problem #2
Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe unopened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
Thank you for any help you can provide me with. !!!!!!!!!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Big plane. At full throttle a light plane flies 275 miles against the wind in the same time it flies 325 miles with the wind. If the plain flies at 120 mph at full throttle in still air, then what is the wind speed?
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Against wind DATA:
distance = 275 ; Rate = (120-wind)mph ; time = 275/(120-w) hrs
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With wind DATA;
distance 325 ; Rate = 120+w mph ; time = 325/(120+w) hrs
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EQUATION:
time = time
275/(120-w) = 325/(120+w)
11/(120-w) = 13/(120+w)
11*120 + 11w = 13*120-13w
24w = 2*120
24w = 240
w = 10 (wind speed)
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Word Problem #2
Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe unopened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
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Drain pipe DATA:
Time = 30 min/job ; Rate = 1/30 job/min
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Inlet pipe DATA:
Comment: If the drain is open for 45 minutes (3/2)tank will flow down
the drain. So to fill the tank in 45 minutes the inlet tank would have
to input (3/2)+1 = (5/2) tank
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Time = 45 min/(5/2)job ; Rate = (5/2)job /45 min = 1/18 job/min
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EQUATION:
Let "x" be the number of minutes it takes to fill the tank when both pipes
are open.
x(1/18-1/30) = 1
x(0.0222222...)=1
x = 45
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Based on your posting this would be the answer BUT the 2nd sentence
in your posting is contradictory; please check it out.
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Cheers,
Stan H.
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