two men starting at a point on a 1mile circular race track w

two men starting at a point on a 1-mile circular race track walk in opposite directions and meet in 6minutes. but if they walk in the same direction, the faster walker gains one lap in 30 minutes. find the speed of each man in miles per hour.

Solution

Let the faster man have a speed of x mph and the slower y.
d=st, s=d/t
s=1/(6/60)
s=10 mph combined speed walking in opposite directions.
.
x-y=2 (x walks 2 miles more than y in 1 hr so he is 2 mph faster.)
x+y=10 (the sum of the distance they walk in 1 hr so there combined speed is 10 mph.)
-----------add
2x=12
.
x=6 mph
y=4 mph