Question 1010832
<pre>
VARIABLE ASSIGMENTS
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y=1.7 hours        time with the wind
x=1.5 hours        time against the wind
d=255 miles        trip distance
r miles per hour   unknown plane speed without any wind
w miles per hour   speed of the wind
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<pre>
                   speed       time      distance
AGAINST Wind       r-w          y          d
WITH Wind          r+w          x          d
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System of equations, {{{system((r-w)y=d,(r+w)x=d)}}}


SOLUTION ALGEBRA STEPS
{{{yr-yw=d}}}
{{{yr=d+yw}}}
{{{r=(d+yw)/y}}}
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substitute into the other equation.
{{{xr+xw=d}}}
{{{x(d+yw)/y+xw=d}}}
{{{xd/y+xyw/y+xw=d}}}
{{{xd/y+xw+xw=d}}}
{{{2xw+xd/y=d}}}
{{{2xw=d-xd/y}}}
{{{w=(1/(2x))(d-xd/y)}}}
{{{highlight(w=d/(2x)-d/(2y))}}}-----This can be evaluated using the assigned values.
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Use the formula for w to find a formula for r.
{{{r=(d+yw)/y}}}
{{{r=(d+y(d/(2x)-d/(2y)))/y}}}
{{{(d+yd/(2x)-yd/(2y))/y}}}
{{{(d+yd/(2x)-d/2)/y}}}
{{{d/y+d/(2x)-d/(2y)}}}
{{{d(1/y+1/(2x)-1/(2y))}}}
{{{d(2x/(2xy)+y/(2xy)-x/(2xy))}}}
{{{highlight(r=d((2x+y-x)/(2xy)))}}}------Evaluate using the variable assignments.