SOLUTION: A jet plane, flying 90 mph faster than a propeller plane, travels 5670 miles in 4 hours less time than the propeller plane takes to fly the same distance. How fast does each plane

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Question 834486: A jet plane, flying 90 mph faster than a propeller plane, travels 5670 miles in 4 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two Unknowns:
r = speed of propeller plane
t = time for propeller plane
constants:
k = 90 mph, a speed difference
h = 4 hour, how much less time needed of the jet
d = 5670 mile trip


PLANE___________speed_________time______________distance
JET_____________r+k___________t-h_______________d
PROPELLER_______r_____________t_________________d

I have already solved a few of this general form travel problem recently, so this will be a very abbreviated solution.

EQUATIONS:
highlight_green%28%28r%2Bk%29%28t-h%29=d%29 and highlight_green%28rt=d%29
Solve this system for r and t. You will get a quadratic equation in either t or r. The way I have solved these, I substituted for t from the simpler equation and first solved for a formula for r. The quadratic equation I had used was in r.