Question 103110
We always start by listing what we know to be equal. In this case, it is the distance driven to/from Amarillo.  Let's call it d.

The standard distance equation is d=rt, where d=distance, r=rate (e.g., velocity), and t=time.

We do not know how long it took to get to Amarillo, but we know it took 4 hours longer to get back. So, let x = time driving to Amarillo and x+4 = time driving back. 

We know r=55 going to Amarillo, and r=30 returning from Amarillo.

dto = 55x
dfrom = 30(x+4)
dto = dfrom (by definition, distance to Amarillo is same as from Amarillo)

So,
55x = 30(x+4)
55x = 30x + 120
Subtracting 30x from both sides
25x = 120
Dividing by 25
x = 4.8 = time spent driving to Amarillo from home
x+4 = 4.8+4 = 8.8 = time spent driving from Amarillo to home

ALWAYS check!
We know dto = dfrom (discussed above), so check the truth of this assertion.
dto=55x=55*4.8=264 miles
dfrom=30(8.8)=264 miles
Check!