parkhydel wrote:
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.
DS23820.02
Target question: From the time she left, how many hours did it take Maria to overtake her husband? Statement 1: Maria drove 60 miles before overtaking her husband. Lots of necessary information is missing here. Consider these two possible scenarios
Case a: The husband's speed is 48 mph. which means he has a 12-mile lead when Maria starts driving. If Maria's speed is 60 mph, she will overtake her husband in 1 hour (and she will have driven 60 miles in the process). In this case, the answer to the target question is
it takes 1 hour for Maria to overtake her husbandCase b: The husband's speed is 60 mph. which means he has a 15-mile lead when Maria starts driving. If Maria's speed is 80 mph, she will overtake her husband in 0.75 hours (and she will have driven 60 miles in the process). In this case, the answer to the target question is
it takes 0.75 hours for Maria to overtake her husbandSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 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.So, Maria's speed = 60 mph
And her husband's speed = 48 mph.
IMPORTANT: At this point we need not perform any lengthy calculations. We need only recognize that we COULD conduct an experiment with all of the given information, and that such an experiment would tell us exactly
how many hours it took Maria to overtake her husband, which means we COULD answer the target question with certainty. So, statement 2 is SUFFICIENT.
Here's what I mean:
We all head over to Maria's house. First, we tell Maria's husband to start driving on some route at a speed of 48 mph. 15 minutes (aka 1/4 hours) later, we start a stopwatch and tell Maria to start driving on the same route at a speed of 60 mph. Once Maria overtakes her husband, we stop the stopwatch, and we now know exactly how long it took Maria to overtake her husband.
Answer: B
Cheers,
Brent