SOLUTION: Hank Hill travels home to Whoville every weekend from Paradise. The distance each way is 800km/h. Anxious to return home, he decides to increase his speed by 20km/h and realizes th

Question 121035: Hank Hill travels home to Whoville every weekend from Paradise. The distance each way is 800km/h. Anxious to return home, he decides to increase his speed by 20km/h and realizes that he arrives home 2 hours earlier than the time it took him to travel to Paradise. How long does the trip to Paradise usually take ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Hank Hill travels home to Whoville every weekend from Paradise. The distance each way is 800 km. Anxious to return home, he decides to increase his speed by 20 km/h and realizes that he arrives home 2 hours earlier than the time it took him to travel to Paradise. How long does the trip to Paradise usually take ?
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Let the usual time to Paradise be "x".
To Paradise DATA:
Distance = 800 km ; Time = x hrs ; Rate = d/t = 800/x kph
--------------------
After changes DATA:
Distance = 800 km ; Time = x-2 hrs ; Rate = d/t = 800/(x-2) kph
-------------------
EQUATION:
New rate - Old rate = 20 km/h
800/(x-2) - 800/x) = 20
40/(x-2) - 40/x = 1
Multiply thru by x(x-2) to get:
40x - 40(x-2) = x(x-2)
80 = x^2-2x
x^2-2x-80=0
x = [2 +- sqrt(4-4*-80)]/2
Find Positive solution:
x = [2 + sqrt(324)]/2
x = [1 + 9]
x = 10 hrs (Usual time to Paradise)
=================
Cheers,
Stan H.
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