There is a really quick way to do this problem. Take the distance as 3 miles which is given. The rates are different by 7 mph - 5.5 mph = 1.5 mph. Now all you need do is find time given these two facts.
Givens:
r = 1.5 mph
t = ???
d = 3 miles
formula
d = r * t
Substitute
3 = 1.5 * t Divide by 1.5
3/1.5 = t
t = 2 hours.
Remark
You could do this the long way.
The time is going to be the same for both runners so find the distance first
Let the distance = x that must be traveled [by the slow runner] before they are together.
Givens fast runner
d = x + 3
r = 7
t = ??
Givens for the slow runner.
d = x
r = 5.5
t = ???
(x + 3)/7 = x/5.5 Cross multiply
5.5(x + 3) = 7x Remove the brackets.
5.5x + 16.5 = 7x Subtract 5.5x from both sides.
16.5 = 7x - 5.5x
16.5 = 1.5x Divide by 1.5
16.5/1.5 = x
x = 11 That means that the slow runner goes 11 miles before the fast runner catches up to him or her.
d = r * t
11 = 5.5 * t
11/ 5.5 = t
t = 2 Same answer, but the short way is easier to do.