Question 350638
Rate*Time=Distance
{{{R*t=D}}}
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For Plane A,
1.{{{R[a]*t=2800}}}
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For Plane B,
2.{{{(R[a]+50)*(t-3)=2200}}}
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From eq. 1,
{{{t=2800/R[a]}}}
Substitute into eq. 2,
{{{(R[a]+50)*(2800/R[a]-3)=2200}}}
{{{(R[a]+50)*(2800-3R[a])=2200*R[a]}}}
{{{2800R[a]-3R[a]^2+140000-150R[a]=2200R[a]}}}
{{{3R[a]^2-450R[a]-140000=0}}}
Use the quadratic formula,
{{{R[a] = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
 {{{R[a] = (450 +- sqrt( (-450)^2-4*3*(-140000) ))/(2*3) }}}
 {{{R[a] = (450 +- sqrt( 202500+1680000 ))/(6) }}}
 {{{R[a] = (450 +- sqrt( 1882500 ))/(6) }}}
Use only the positive answer.
{{{R[a] = (450 + 1372))/(6) }}}
{{{highlight(R[a]=303.7)}}}kph
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{{{R[b]=303.7+50}}}
{{{highlight(R[b]=353.7)}}}kph