Two hikers are 13 miles apart and walking torward each other. They meet in 2 hours. Find the rate of each hiker if one hiker walks 2.1 mph faster than the other one.

Meet in 2 hours

means that the distance covered over 2 hours adds to total distance which is 13miles

basically, imagine instead of moving in oposite directions, toward each other, imagine that one moves for 2 hours then theh other one moves for another 2 hours, total 13 miles

so

speed1=x

speed2=y

x is 2.1 more than y

x=2.1+y

distance=speed times time

time=2hours

speed=x and y

total distance=13

13=2x+2y

x=2.1+y

sub

13=2 (2.1+y) + 2y

13=4.2+2y+2y

13=4.2+4y

minus 4.2 from both sides

8.8=4y

divide both sides by 4

2.2=y

sub

x=2.1+y

x=2.1+2.2

x=4.3

the hikers hiked 2.2mph and 4.3mph