SOLUTION: A jet plane, flying 80 mph faster than a propeller plane, travels 3960 miles in 2 hours less time than the propeller plane takes to fly the same distance. How fast does each plane

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Question 992214: A jet plane, flying 80 mph faster than a propeller plane, travels 3960 miles in 2 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A jet plane, flying 80 mph faster than a propeller plane, travels 3960 miles in 2 hours less time than the propeller plane takes to fly the same distance.
How fast does each plane fly?
:
let s = the speed of the prop plane
then
(s+80) = speed of the jet
:
Write a time equation; time = dist/speed
Prop time - jet time = 2 hrs
3960%2Fs - 3960%2F%28%28s%2B80%29%29 = 2
multiply the equation by s(s+80)
s(s+80)*3960%2Fs - s(s+80)*3960%2F%28%28s%2B80%29%29 = 2s(s+80)
cancel the denominators and you have
3960(s+80) - 3960s = 2s^2 + 160s
3960s + 316800 - 3960s = 2s^2 + 160s
combine to form a quadratic equation
0 = 2s^2 + 160s - 316800
simplify divide by 2
s^2 + 80s - 158400 = 0
you can use the quadratic formula to find s a=1; b=80; c=158400
but this will factor
(s+440)(s-360) = 0
the positive solution
s = 360 mph is the speed of the prop plane
the jet 80 mph faster, hence
440 mph is speed of the jet
:
:
Check this by finding the actual time of each plane
3960/360 = 11 hrs for prop to make the trip
3960/440 = 9 hrs for the jet