Question 159072
For each part of the trip,
{{{d[1] = r[1]*t[1]}}} and,
{{{d[2] = r[2]*t[2]}}}
given:
{{{d[1] = 81}}}mi
{{{d[2] = 18}}}mi
{{{r[2] = r[1] - 5}}} mi/hr
{{{t[1] + t[2] = 5}}} hr
{{{t[2] = 5 - t[1]}}}hr
------------------
{{{d[1] = r[1]*t[1]}}}
{{{81 = r[1]*t[1]}}}
(1){{{r[1] = 81/t[1]}}}
{{{18 = r[2]*t[2]}}}
{{{18 = (r[1] - 5)*(5 - t[1])}}}
{{{18 = 5r[1] - 25 - r[1]*t[1] + 5t[1]}}}
------------------
note that {{{r[1]*t[1] = 81}}}, so
{{{18 = 5r[1] - 25 - 81 + 5t[1]}}}
{{{5r[1] + 5t[1] = 106 + 18}}}
{{{5r[1] + 5t[1] = 124}}}
Substituting from (1) above,
{{{5*(81/t[1]) + 5t[1] - 124 = 0}}}
multiply both sides by {{{t[1]}}}
{{{5 + 5*(t[1])^2 - 124t[1] = 0}}}
rearranging,
{{{5(t[1])^2 - 124t[1] + 5 = 0}}}
Solve this using the quadratic equation to find {{{t[1]}}}
Then use that to find {{{r[1]}}} and {{{r[2]}}}