Question 830872: a jet plane flying 100 mph faster than a propeller plane, travels 3150 miles in 2 hours less time than the propeller plane takes to fly the same distance. what are the speeds of both planes?
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! r for speed of the propeller plane
h for the time of the propeller plane
Rate*Time=Distance
___________________speed_____________time______________distance
PROP_______________r__________________h__________________3150
JET_______________r+100_____________h-2__________________3150
Immediately find two equations:
 and  ;
'
Working with the jet equation,
rh+100h-2r-200=3150
And substituting using the first equation
3150+100h-2r-200=3150
r-50h+100=0
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Now, solving the propellor equation for h, find  , and substitute into jet equation as just found,  ,
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some steps
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Not shown here next, but use of general solution to the quadratic equation will give you ....
 mph
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SUMMARY:
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Propeller plane, r=350 mph
Jet plane, r+100=450 mph
Travel time propeller, h=9 hour
Travel time jet, h-2=7 hours
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