The data sufficiency question asks the following: "How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?"

(1) If Betty's average speed for the trip had been 1.5 times as fast, the trip would have taken 2 hours.

(2) Betty's average speed for the trip was 50 miles per hour.

The correct answer is A, because (3/2)r times (2/3)t = rt, and 2t/c = 2 . Could you explain how the first equation transformed into the second equation (i.e. 2t/c = 2)?

If Betty's average speed for the trip had been 1.5 times as fast, the trip would have taken 2 hours

We know that for her actual trip, RT=D (where R is her actual rate, T is her actual time and D is her actual distance.)

Now, from the first statement, we know that if her rate had been 1.5R instead of R (1.5R = (3/2)R) then her time would have been 2 instead of T. Since we're dealing with the same trip, our D is still just D.

Here's what we get:
1.5R * 2 = D
3R/2 * 2 = D
3R = D

Since we know that RT=D AND that 3R=D, we know that RT = 3R. This tells us that T=3, and this is what they asked in the original question.

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