Question 831367: A jet plane, flying 160 mph faster than a propeller plane, travels 4800 miles in 5 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! This general type of travel problem seems to be becoming common.
A jet plane, flying v mph faster than a propeller plane, travels d miles in p hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly? Assume v and p are positive numbers.
Additionally, let r be the speed of the propeller plane; and let h be the time for the propeller plane to make the d distance.
_______________speed___________time________________distance
JET____________r+v____________h-p__________________d
PROP____________r______________h___________________d
The UNKNOWN variables are r and h. Use the uniform rates equation for travel, R*T=D, for Rate, Time, Distance.
EQUATIONS TO BEGIN:
 , and  ;
The steps will very neatly give a useful equation...
...starting with the jet's equation.
Notice that we already have the propeller plane's equation rh=d allowing a substitution:
We can again use the propeller's simple equation, as  , and then get
 -----QUADRATIC EQUATION IN THE ONE VARIABLE, r. Use general solution to a quadratic equation to solve for r. Use found value to get the value for h.
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