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 t

Algebra ->  Radicals -> 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 t      Log On


   

Question 149080: 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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?
:
Let s = Leon's speed
then
(s+10) = Pat's speed
:
Write a time equation: Time = dist%2Fspeed
:
Leon's time = Pat's time
270%2Fs = 330%2F%28%28s%2B10%29%29
Cross multiply:
:
330s = 270(s+10)
:
330s = 270s + 2700
:
330s - 270s = 2700
:
60s = 2700
:
s = 2700%2F60
s = 45 mph is Leon's speed
then
55 mph is Pat's speed
;
:
Check solution; confirm that the times are equal
(330)/55 = 6 hrs
(270)/45 = 6 hrs