SOLUTION: A plane traveled a distance of 800 miles and returned the same distance. If the rate returning is 40 miles per hour faster than the rate going, and if the total flight took 8 hours

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Question 380432: A plane traveled a distance of 800 miles and returned the same distance. If the rate returning is 40 miles per hour faster than the rate going, and if the total flight took 8 hours, how fast did the plane travel on the return trip?
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A plane traveled a distance of 800 miles and returned the same distance. If the rate returning is 40 miles per hour faster than the rate going, and if the total flight took 8 hours, how fast did the plane travel on the return trip?
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Going DATA:
distance = 800 miles ; rate = x mph ; time = 800/x hrs
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Return DATA:
distance = 800 miles ; rate = (x+40) mph ; time = 800/(x+40) hrs
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Equation:
time + time = 8 hrs.
800/x + 800/(x+40) = 8
800(x+40) + 800x = 8x(x+40)
1600x + 32000 = 8x^2+320x
8x^2- 1280x -32000 = 0
x^2 - 160x - 4000 = 0
Positive solution:
x = 181.98 mph
x+40 = 221.98 mph (return leg speed)
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Cheers,
Stan H.

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Distance = 800 miles . speed going = x mph
distance = 800 miles : speed = x+40 mph.
...
time going +time returning=8
..
t=d/r
800/x+800/(x+40 )= 8
..
lcd = x(x+40)
800(x+40)+800x /x(x+40)=8
800x+32000+800x=8x^2+320x
8x^2-1600x+320x-32000=0
8x^2-1280x-32000=0
/8
x^2-160x-4000=0
..
find the roots x1,x2 using quadratic formula
discriminant = 41600
x1=((160+sqrt(41600))/2
x1= 181.98 = 182 mph
x2 is negative so reject.
return trip speed = x+40 = 182 +40 = 222 mph
...
m.ananth@hotmail.ca