Question 830872
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:
{{{rh=3150}}} and {{{(r+100)(h-2)=3150}}};

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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 {{{h=3150/r}}}, and substitute into jet equation as just found, {{{r-50h+100=0}}},
{{{r-50(3150/h)+100=0}}}
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some steps
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{{{highlight_green(r^2+100r-157500=0)}}}
Not shown here next, but use of general solution to the quadratic equation will give you ....
{{{highlight(r=350)}}} 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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