This GMAT DS question is on speed and time — I’m not sure how to solve it without doing full calculations.?

Question

Maria left home 1/4  hour after her husband and drove over the same route as he had in order to overtake him. From the time she left, how many hours did it take Maria to overtake her husband? 
1. Maria drove 60 miles before overtaking her husband.

2. While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband’s average rate.

S Raghav · Accepted Answer

With GMAT Data Sufficiency questions like this, you don&rsquo;t always need to calculate the exact answer,  just figure out whether you have enough information to get a unique value.
Statement 1 says Maria drove 60 miles before overtaking her husband. But without knowing her speed or his, we can&rsquo;t tell how long that took. She could&rsquo;ve driven fast or slow, so this alone isn&rsquo;t enough.
Statement 2 tells us Maria drove at 60 mph and her husband was driving 12 mph slower, so 48 mph. It also tells us she left &frac14; hour later. That&rsquo;s enough to set up a single equation: since she&rsquo;s closing the gap at a rate of 12 mph (the speed difference), and he had a &frac14;-hour head start, she needs to make up that lead , which happens in 1 hour. So statement 2 alone is sufficient.
Answer is B ,  only statement 2 is sufficient.

Divakshi Arora · Answer

This is a classic relative speed setup , here&rsquo;s how to think through it:

Statement 1 gives distance but no speed, so time can&rsquo;t be determined uniquely
Statement 2 gives Maria&rsquo;s speed and her husband&rsquo;s (60 vs. 48 mph) and the 1/4 -hour head start
Use relative speed: Maria gains on him at 12 mph
He had a 1/4-hour &times; 48 mph = 12-mile lead
She catches up in 1 hour (12 miles &divide; 12 mph gain rate)

So only Statement 2 is sufficient.  Final answer is B.