Question 82051
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