Question 235021
You need 2 equations, 1 for each part of the trip
{{{d[1] = r[1]*t[1]}}}
{{{d[2] = r[2]*t[2]}}}
given:
{{{d[1] = 60}}} mi
{{{d[2] = 46}}} mi
{{{t[2] = t[1] + 1}}} hrs
{{{r[2] = r[1] - 4}}} mi/hr
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Now I can rewrite the equations
(1) {{{60 = r[1]*t[1]}}}
(2) {{{46 = (r[1] - 4)*(t[1] + 1)}}}
This is 2 equations and 2 unknowns, so it's solvable
(2) {{{46 = r[1]*t[1] - 4t[1] + r[1] - 4}}}
And, since {{{60 = r[1]*t[1]}}},
(2) {{{46 = 60 - 4t[1] + r[1] - 4}}}
(2) {{{r[1] - 4t[1] + 10 = 0}}}
Now go back to (1)
(1) {{{60 = r[1]*t[1]}}}
{{{t[1] = 60/r[1]}}}
plug this back into (2)
(2) {{{r[1] - 4*(60/r[1]) + 10 = 0}}}
Multiply both sides by {{{r[1]}}}
{{{r[1]^2 - 240 + 10r[1] = 0}}}
{{{r[1]^2 + 10r[1] - 240 = 0}}}
This can be solved by completing the square
{{{r[1]^2 + 10r[1] + (10/2)^2 = 240 + (10/2)^2}}}
{{{r[1]^2 + 10r[1] + 25 = 240 + 25 }}}
The left side is a perfect square
{{{(r[1] + 5)^2 = 265}}}
Take the square root of both sides
{{{r[1] + 5 = sqrt(265)}}}
{{{r[1] = sqrt(265) - 5}}} mi/hr
And, since
{{{r[2] = r[1] - 4}}}
{{{r[2] = sqrt(265) - 5 - 4}}}
{{{r[2] = sqrt(265) - 9}}} mi/hr