Help on word problem

Question

At 10:00 AM two people set out to meet each other from towns 28 miles apart. One bicycle travels 3 miles per hour faster than the other. If they meet at 11:20 AM, what is the speed of each bicycle?

Answer 1

1 hr 20 min trip

one 3 mph faster

slower one went x mph for t hours x=20 mph t=8/9 of an hour = 160/3 = 53 minutes 20 seconds

faster one went x+3 mph for 4/3-t hours x+3 = 23 mph, 4/3-t = 4/9 of an hour = 80/3= 26 min 40 sec

distance = 28 miles = d = rt = (x)(t) + (x+3)(4/3 -t)

28 = xt + -xt -3t+ 4 + 4x/3

24= 4x/3 -3t

72 = 4x -9t

average speed = 28/4/3 =21 mph

23 for fast guy 20 for slower

4(20) - 9t = 72

9t = 80-72=8

t =8/9

T=4/9

20x8/9 + 23x4/9 = (160+92)/9 = 252/9 =28 miles