Question 324046
Rate*Time=Output
{{{Rj(T-6)=1}}}
{{{Rj=1/(T-6)}}}
{{{Rs(T)=1}}}
{{{Rs=1/T}}}
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{{{(Rj+Rs)4=1}}}
{{{Rj+Rs=1/4}}}
{{{1/(T-6)+1/T=1/4}}}
{{{4T/(T(T-6))+(4(T-6))/(T(T-6))=T(T-6)/(T(T-6))}}}
{{{4T+4T-24=T^2-6T}}}
{{{T^2-14T-24=0}}}
Use the quadratic formula,
{{{T = (14 +- sqrt(14^2-4*1*(-24) ))/(2*1) }}}
{{{T = (14 +- sqrt(196+96 ))/2 }}}
{{{T = (14 +- sqrt(292))/2 }}}
{{{T = (14 +- 2sqrt(73))/2 }}}
{{{T = 7 +- sqrt(73) }}}
Only the positive value makes sense for our problem.
It takes Skyler {{{T}}} hrs or {{{7+sqrt(73)}}} hrs.
It takes Jake {{{T-6}}} hrs or {{{1+sqrt(73)}}} hrs.