A man drives 600 miles to a convention on the return trip he

A man drives 600 miles to a convention. on the return trip he increases his speed by 10 mph and saves 2 hours driving time. how fast did he drive going to and from the convention?

Solution

(600/x)-2=600/(x+10)
(600-2x)/x=600/(x+10) cross multiply
(600-2x)(x+10)=600x
600x-2x^2-20x+6000=600x
2x^2+20x-6000=0
x^2+10x-3000=0
(x+60)(x-50)=0
x-50=0
x=50 for the speed going to the convention
50+10=60 return trip speed.
proof
(600/50)-2=600/60
12-2=10
10=10