SOLUTION: going skiing leon drove 270 miles to the lodge in the same time as pat drove 330 miles to the lodge. If pat drove 10 miles per hour faster than leon, then how fast did each of them

Question 82051: going skiing leon drove 270 miles to the lodge in the same time as pat drove 330 miles to the lodge. If pat drove 10 miles per hour faster than leon, then how fast did each of them drive.
Please give step by step instructions
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
distance(d) equals rate(r) times time(t) or d=rt;t=d/r and r=d/t
Let r=Leon's rate of speed
then r+10=Pat's rate of speed
Time it took Leon to make the trip=d/r=270/r
Time it took Pat to make the trip=d/r=330/(r+10)
We are told that they both drove to the lodge in the same amount of time. So:
270/r=330/(r+10) multiply both sides by r(r+10) to get rid of the fractions (this is equivalent to cross multiplying)
270(r+10)=330r get rid of parens
270r+2700=330r subtract 270r from both sides
270r-270r+2700=330r-270r collect like terms
60r=2700 divide both sides by 60
r=45 mph-----------------------------------Leon's rate of speed
r+10=45+10=55 mph------------------------------Pat's rate of speed
CK
For Leon t=d/r; t=270/45=6 hrs
For Pat t=d/r; t=330/55=6 hrs

Hope this helps---ptaylor

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