Question 972570
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Let r=the rate of Flight 237
Between noon and 3:00pm (3 hours), Flight 237 travels 3hrs(r) miles.
Flight 875 travels 3hrs(r-40mph)
These two distances form a right triangle with hypotenuse=600 miles.
{{{(3hrs(r))^2+(3hrs(r-40))^2=600^2}}}
{{{(9r^2)+(3r-120)^2=360000}}}
{{{9r^2+9r^2-720r+14400=360000}}}
{{{18r^2-720r-345600=0}}}
{{{r^2-40r-19200=0}}}
{{{(r-160)(r+120)=0}}}
{{{r-160=0}}} {{{or}}} {{{r+120=0}}}
{{{r=160}}} {{{or}}} {{{r=-120}}}
The rate of Flight 237 was 160 mph.
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CHECK:
The rate of Flight 237 was 160 mph, so its distance was 480 miles.
The rate of Flight 875 was 120 mph, so its distance was 360 miles .
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{{{(480mi)^2+(360mi)^2=(600mi)^2}}}
{{{230400mi^2+129600mi^2=360000mi^2}}}
{{{360000mi^2=360000mi^2}}}