Distance and Rate Problems in Data Sufficiency

This is a “Value” DS question. The Value we are looking for is the time it took Bob to finish. Let’s look at the specific wording:

How long did it take Bob to complete the race?

(1) If Bob were 2/3 faster, his time would have been 3 hours.
(2) Bob’s average speed was 30 miles per hour.

Given information: We know that Distance = Rate x Time, so if we knew Distance/Rate, then we could find the Time. We could think of this question as asking, what is the ratio between Bob’s Distance and Bob’s Rate?

Need: Distance/Rate

Statement (1):

We know D = R x T.
This says that (5/3)D = R x 3.

Let’s simplify:
(5/3)D = 3R
5D = 9R
D/R = 9/5

Sufficient! We found the ratio we were looking for!

Statement (2):

Average Speed = Total Distance / Total Time
30 = D/T

Unfortunately, we cannot find T. This is insufficient.

The answer is (A).