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