On the trip from Detroit to Columbus, Ohio, Mrs. Smith drove an average speed of 60 mph. Returning, her average speed was 55 mph. If it took her 1/3 of an hour longer on the return trip, how far is it from Detroit to Columbus?

Remember that Distance = (Average speed)(Time)
Let x be the distance between Detroit and Columbus. 
We know the journey from Detroit to Columbus  took a time t, and the returning trip took a time t+[tex] \frac{1}{3} [/tex]. We also know the Average speed of both journeys, so now we can set our equations:
[tex] \left \{ {{x=60t} \atop {x=55(t+ \frac{1}{3}) }} \right. [/tex]
Now, we can replace equation 1 into equation 2 to find t:
[tex]60t=55(t+ \frac{1}{3} )[/tex]
[tex]60t=55t+ \frac{55}{3} [/tex]
[tex]5t= \frac{55}{3} [/tex]
[tex]t= \frac{11}{3} [/tex]

Now that we know t, we can replace it into our equation 1 to get the distance:
[tex]x=(60)( \frac{11}{3} )[/tex]
[tex]x=220[/tex]

We can conclude that the distance between Detroit and Columbus is 220 miles.