Bunuel wrote:
Tom and Samuel are riding motorcycles down the highway at constant speeds. If Tom is now 2 miles ahead of Samuel, how many minutes before Tom is 3 miles ahead of Samuel?
(1) Tom is traveling at 70 miles per hour and Samuel is traveling at 60 miles per hour.
(2) Tom left 5 minutes before Samuel.
Question Stem Analysis:We are told that Tom and Samuel are riding at constant speeds, and Tom is 2 miles ahead of Samuel. We need to determine the number of minutes after which Tom will be 3 miles ahead of Samuel. In other words, we need to find the number of minutes for Tom to increase the distance between the two drivers by 1 mile.
Statement One Alone:\(\Rightarrow\) Tom is traveling at 70 miles per hour and Samuel is traveling at 60 miles per hour.
Thus, the distance between Tom and Samuel is increasing at a rate of 70 - 60 = 10 miles per hour. If the distance increases by 10 miles each hour, then the distance between the two drivers will increase by 1 mile in 1/10 \(\times\) 60 minutes = 6 minutes. So, Tom will be 3 miles ahead of Samuel in 6 minutes. Statement one is sufficient.
Eliminate answer choices B, C, and E.
Statement Two Alone:\(\Rightarrow\) Tom left 5 minutes before Samuel.
Without knowing anything about the speeds of each driver or the difference between the speeds of the two drivers, we cannot determine the number of minutes for Tom to increase the distance to 3 miles. For instance, if Tom travels at 70 mph and Samuel travels at 60 mph, then Tom will be 3 miles ahead of Samuel in 6 minutes, as we calculated earlier. On the other hand, if Tom travels at 80 mph and Samuel travels at 60 mph, then the distance between the two drivers will increase by 80 - 60 = 20 miles per hour. Thus, Tom will be 3 miles ahead of Samuel in 1/20\(\times\) 60 minutes = 3 minutes. Since there is more than one possible answer to the question, statement two alone is not sufficient.
Note that as long as we know Tom is 2 miles ahead of Samuel, the fact that Tom left 5 minutes earlier than Samuel is not relevant in our calculations.
Answer: A