SOLUTION: A jet plane, flying 150 mph faster than a propeller plane, travels 5280 miles in 5 hours less time than the propeller plane takes to fly the same distance. How fast does each plane

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Question 832546: A jet plane, flying 150 mph faster than a propeller plane, travels 5280 miles in 5 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 150 mph faster than a propeller plane, travels 5280 miles in 5 hours less time than the propeller plane takes to fly the same distance.
How fast does each plane fly
:
Let s = propeller plane speed
then
(s+150) = the jet plane speed
:
Write a time equation, time = dist/speed
prop time - jet time = 5 hrs
5280%2Fs - 5280%2F%28%28s%2B150%29%29 = 5
Multiply equation by s(s+150), cancel the denominators and you have
5280(s+150) - 5280s = 5s(s+150)
5280s + 792000 - 5280s = 5s^2 + 750s
Combine on the right as a quadratic equation
0 = 5s^2 + 750s - 792000
simplify divide by 5
s^2 + 150s - 158400 = 0
You can use the quadratic formula here, but this will factor to
(s+480)(s-330) = 0
The positive solution
s = 330 mph is speed of the prop plane
:
You can find the speed of the jet. Find the actual time of each to check your answer.