Question 1159329
Bert traveled 72 miles across the state through rain at a reasonable speed.
 If it had been sunny, he would have driven an average of 20 miles per hour faster, and would have arrived at his destination 24 minutes sooner.
:
let s = speed in the rain
let t = drive time in the rain
change 24 min 24/60 = .4 hrs, then
(s+20) = sunny speed
(t-.4) = sunny driving time)
Two distance equations
s*t = 72
for substitution
s = 72/t
and
(t-.4)*(s+20) = 72
FOIL
ts + 20t - .4s - 8 = 72
we know ts = 72
72 + 20t - .4s - 8 = 72
-72 from both sided 
20t - .4s - 8 = 0
simplify, divide by .4
50t - s - 20
replace s with (72/t)
50t - 72/t - 20 = 0
multiply by t
50t^2 - 72 - 20t = 0
A quadratic equation
50t^2 - 20t - 72 = 0
Using the quadratic formula I got a postive solution of
t = 1.41655 hrs or 1 + .41655*60 = 1 hr 25 min, his time in the rain
:
  How fast was he driving in the rain?
{{{72/1.41655}}} = 50.8 mph 
:
:
Check this, find his sunny speed. 50.8 + 20 = 70.8 mph
Find his sunny time: {{{72/70.8}}} = 1.0169 or 1 + .0169*60 = 1 hr 1 min
Which ia 24 min faster than the time in rain



Hint: First solve a quadratic equation. Then write two equations with two unknowns.