Question 179409
(1) {{{150 = r*t}}}
(2) {{{150 = (r + 20)*(t - 2)}}}
Subtract (1) from (2)
{{{0 = (r + 20)(t - 2) - r*t}}}
{{{r*t = r*t + 20t - 2r - 40}}}
{{{2r = 20t - 40}}}
And, since 
{{{150 = r*t}}}
{{{t = 150/r}}}
{{{2r = 20*(150/r) - 40}}}
{{{2r^2 = 3000 - 40r}}}
{{{2r^2 + 40r - 3000 = 0}}}
{{{r^2 + 20r - 1500 = 0}}}
Solve by completing the square
{{{r^2 + 20r + (20/2)^2 = 1500 + (20/2)^2}}}
Notice the left side is a perfect square
And so is the right side
{{{(r + 10)^2 = 1600}}}
Take the square root of both sides
{{{r + 10 = 40}}}
{{{r = 30}}}
The speed is 30 mi/hr
 check:
(1) {{{150 = 30*t}}}
{{{t = 5}}} hrs
(2) {{{150 = (r + 20)*(t - 2)}}}
(2) {{{150 = (30 + 20)*(t - 2)}}}
(2) {{{150 = 50*(t - 2)}}}
{{{3 = t - 2}}}
{{{t = 5}}} hrs
OK