Question 1136702
{{{highlight_green(200/r+160/(r-30)=6)}}}


r, car speed on main highway


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r, speed
x, time
d, distance
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{{{system(rx=d,x=d/r)}}}


<pre>
                       SPEEDS        TIMES        DISTANCES

Main hwy               r            200/r          200

Secondary hwy          r-30         160/(r-30)     160

TOTAL                                6
</pre>
Sum of the time quantities totals 6 hours.


{{{200/r+160/(r-30)=6}}}

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{{{100/r+80/(r-30)=3}}}

{{{100(r-30)+80r=3r^2-90r}}}

{{{270r-3000=3r^2}}}

{{{90r-1000=r^2}}}

{{{r^2-90r+1000=0}}}

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{{{highlight(r=77)}}}