There are already excellent solutions for this question in this thread, but I thought I would offer up an alternative solution for those who may prefer to work with numbers rather than algebra. This involves using a table to organize the information, which some people may find faster and less confusing than setting up an algebraic equation. Here are the specific GMAT Timing Tips that I suggest for this question (the links have growing lists of questions that you can use to practice each tip):
Use D = R x T and W = R x T on rate problems: Like nearly every distance rate and work rate problem, this question will probably go more quickly if you remember to use the appropriate rate equation, in this case D = R x T (Distance = Rate x Time).
Use relative rates when two objects are moving: Notice that Al and Ben are moving in opposite directions, so their relative rate of motion — the rate at which the distance is changing between them — is the sum of their rates: 20 miles/hour + 40 miles/hour = 60 miles/hour. We can also think of this as the rate at which they collectively cover distance while they are both moving.
Use tables to organize rate problems with multiple scenarios: While it is possible to go straight to writing an equation to solve this problem, some may find it faster and less confusing to organize the information for this problem in a table. The columns of the table are Distance, Rate, and Time, remembering that Distance = Rate x Time. Each row of the table represents one of the two scenarios in this question: The first row represents the period 8-11am when only Ben is driving, and the second row represents the period after 11am when both Al and Ben are driving. The table that I created for this problem is shown below. Note that I filled in the boxes in the table in this order:
1) The total distance (below the table) is 240 miles, so the distances in the two rows above must add up to 240 miles.
2) The time for 8-11am is 3 hours.
3) The rate for 8-11am is 20 miles/hour (Ben’s speed).
4) Because Distance = Rate x Time, the distance for 8-11am is 60 miles.
5) Because the total distance must be 240 miles, the distance for 11am-? must be 240 – 60 = 180 miles.
6) The rate for 11am-? is 20 + 40 = 60 miles/hour (the sum of Al’s and Ben’s speeds).
7) Because Distance = Rate x Time, the time for 11am-? is (180 miles) / (60 miles/hour) = 3 hours. Thus, the answer is 3 hours after 11am, or 2:00 p.m.
Please let me know if you have any questions, or if you would like me to post a solution video!