SOLUTION: Hi, Need some help on this word problem .. thank you Solve the problem by using a proportion (fraction): Leon drove 270 miles to the lodge in the same time as Pat drove 330 mil

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi, Need some help on this word problem .. thank you Solve the problem by using a proportion (fraction): Leon drove 270 miles to the lodge in the same time as Pat drove 330 mil      Log On


   

Question 7335: Hi, Need some help on this word problem .. thank you
Solve the problem by using a proportion (fraction):
Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove ten miles per hour faster than Leon, then how fast did each of them drive?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Using d+=+rt as a basis and since the time, t, is the same for both travellers. you can set up the proportion as follows:
d1%2Fr1+=+d2%2Fr2 Where: d1 = 270 miles, d2 = 330 miles, r1 is Leon's speed and r2 is Pat's speed.
But, Pat's speed (r2) is 10 mph more than Leon's speed. So, r2 = r1 + 10
270%2Fr1+=++330%2F%28r1%2B10%29 Cross-multiply.
270%28r1%2B10%29+=+330%28r1%29 Simplify and solve for r1 (Leon's speed)
270r1+%2B+2700+=+330r1 Subtract 270r1 from both sides.
2700+=+60r1 Divide both sides by 60.
45+=+r1
Leon's speed is 45 mph.
Pat's speed is 45 mph + 10 mph = 55 mph.
Check:
The travel times should be the same for both travellers.
Leon's tims: t1+=+270+miles%2F45+mph = 6 hours
Pat's time: t2+=+330+miles%2F55+mph = 6 hours.