## While on a straight road, car X and car Y…

## Solution:

We are given that car X and car Y are traveling on a straight road at different constant rates. We also are given that car X is now 1 mile ahead of car Y. We must determine the number of minutes it takes for car X to be 2 miles ahead of car Y.

Although the problem is not technically a Catch-up and Pass Problem, we can use the same formula we would normally use in a catch-up and pass problem to determine the time it takes car X to be 2 miles ahead of car Y.

Thus, we can use the formula:

Time = (change in distance)/(difference in rates)

For car X to be 2 miles ahead of car Y where it was originally 1 mile ahead, the change in distance is 2 – 1 = 1 mile. The difference in rates is car X’s rate – car Y’s rate. Therefore,

Time = 1 / (car X’s rate – car Y’s rate)

We see that if we can determine the difference between the rates of car X and car Y, we can determine how many minutes it will take car X to be 2 miles ahead of car Y.

**Statement One Alone: **

Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.

Using the information in statement one, we see the difference in rates between car X and car Y is 50 – 40 = 10 mph. Thus, we can determine the time it takes car X to be 2 miles ahead of car Y.

Time = 1 / (car X’s rate – car Y’s rate)

Time = 1 /10

It takes car X 1/10 hour, or 6 minutes, to be 2 miles ahead of car Y. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

3 minutes ago car X was 1/2 mile ahead of car Y.

Since car X was ½ mile ahead of car Y 3 minute ago, and is now 1 mile ahead of car Y, we can determine that the difference between the rates of car X and car Y is ½ mile per 3 minutes, or (1/2)/3 = 1/6 mile per minute. Thus, we can determine the time it takes car X to be 2 miles ahead of car Y.

Time = 1 /(1/6)

Time = 6 minutes

Statement two alone is also sufficient to answer the question.

**Answer:** D