Question 314426
Rate*Time=Distance
{{{ R1*T1=D1 }}}
{{{R1*T1=12}}}
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{{{R2*T2=8}}}
{{{R2=R1+1}}}
{{{(R1+1)*T2=8}}}
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You also know that
{{{T1+T2=6}}}
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From above,
{{{T1= 12/R1}}}
{{{T2 = 8/(R1+1)}}}
Substitute,
{{{T1+T2=6}}}
{{{ 12/R1+8/(R1+1)=6}}}
{{{12(R1+1)+8R1=6R1(R1+1)}}}
{{{12R1+12+8R1=6R1^2+6R1}}}
{{{6R1^2-14R1-12=0}}}
{{{(6R1+4)(R1-3)=0}}}
Two solutions but only positive solution makes sense in this problem.
{{{R1-3=0}}}
{{{R1=3}}}
Then from above,
{{{highlight_green(R2=4)}}}