Question 149080
 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/speed}}}
:
Leon's time = Pat's time
{{{270/s}}} = {{{330/((s+10))}}}
Cross multiply:
:
330s = 270(s+10)
:
330s = 270s + 2700
:
330s - 270s = 2700
:
60s = 2700
:
s = {{{2700/60}}}
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