Question 993575
rate * time = distance.


let r = rate going to the mountains.
let r + 20 = rate coming back from the mountains.


going time = 12 hours, so rate * time = distance becomes:


rate * 12 = distance


coming back time = 8 hours, so rate * time = distance becomes:


(rate + 20) * 8 = distance.


let r = rate and d = distance and your formulas become:


r * 12 = d
(r + 20) * 8 = d


simplify the second equation to get:


r * 8 + 20 * 8 = d


simplify it further to get:


r * 8 + 160 = d


your two equations are now:


r * 12 = d
r * 8 + 160 = d


subtract the second equation from the first equation and you get:


r * 4 - 160 = 0


add 160 to both sides of the equation to get:


r * 4 = 160


divide both sides of the equation by 4 to get:


r = 40


if r = 40, then r + 20 = 60


she traveled at 40 miles per hour going and 60 miles per hour coming back.


12 * 40 = 480


8 * 60 = 480


distance is 480 miles.