Re: While on a straight road, Car X and Car Y are traveling at
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16 Oct 2021, 10:49
While on a straight road, Car X and Car Y are traveling at different constant rates. If Car X is now 1 mile ahead of Car Y, how many minutes from now will Car X be 2 miles ahead of Car Y ?
(1) Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour.
(2) Three minutes ago Car X was 1/2 mile ahead of Car Y.
Analyzing the question stem, we learn a few things. Car X and Y are traveling at constant rates. Car X is 1 mile ahead of Car Y now, clarifying that they're moving in the same direction (from the word "ahead of"), and maybe was behind Car Y at some point. The question asks how many minutes from now will Car X be 2 miles ahead of Car Y, a specific value. So, for an answer to be sufficient, I need to know one value.
Before I look at the statements, I think to myself, a sufficient statement might give me either X and Y's individual rates, or the difference between their rates.
Statement 1 - Sufficient.
This gives me Car X's rate and Car Y's rate. I could use these to figure out the time, perhaps by making a chart of X and Y's distance at 1 min, 2 mins, 3 mins, etc to find where X distance traveled is 2 greater than Y's distance traveled (turns out, it's 6 minutes from now).
Statement 2 - Sufficient.
Taking the question stem and this statement together, I know that 3 minutes ago, Car X was 1/2 mile ahead, and now, 3 minutes later, Car X is 1 mile ahead. Therefore, every 3 minutes, Car X gains 1/2 mile on Car Y. This information is sufficient to say how long it'll be before Car X is 2 miles ahead because I understand the difference between Car X's rate and Car Y's rate. This statement is sufficient. Specifically, I know that in another 3 minutes, Car X will be 1+1/2 miles ahead, and in another 3 minutes from there, Car X will be 2 miles ahead, so in 6 minutes (2x3), Car X will 2 miles ahead of Y.