While on a straight road, Car X and Car Y are traveling at

Hello Kimberly77

In order to help you understand Statement 2 better, I will take you through the entire solution. This way the flow shall be consistent and any other doubt you may have regarding the solution will also get resolved.

Question-Stem Analysis

“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 ?”

Given:

• Car X and Y are travelling on a straight road.
• The speeds of car X and car Y are constant and different from one another.
• Car X is presently 1 mile ahead of Car Y.

From the given information we can infer that car X and Y must be travelling in the same direction since car X is ahead of car Y. Car X would not be said to be ahead of car Y if they were moving in opposite directions.

Asked:

• After how many minutes from now (from the point when the distance between X and Y is 1 mile), will the distance between X and Y grow to 2 miles (the gap will increase by 1 mile).
  
  • So, we have to find the time t (in minutes) in which car Y shall move by d miles and car X shall move by (d + 1) miles, so that the gap between X and Y increases by 1 mile.
  • In other words, ‘t’ is the time in which car X will travel an additional 1 mile compared to car Y.
  • If any of the Statements can give a definite value of “t”, the statement will be sufficient.

To find this, we must know the speed of car X relative to the speed of car Y. That is, how fast car X is compared to car Y.

Suppose car X travels at S¬1 miles/h and car Y travels at S2 miles/h where S1 > S2.

• So, car X travels S1 miles in 1 hour. Similarly, car Y travels S2 miles in 1 hour.
• Thus, car X travels an additional (S1 – S2) miles more than car Y in 1 hour.
  
  • Hence, by unitary method, we can find that if car X travels (S1 – S2) miles more than car Y in 1 hour, then in how much time would it travel 1 mile more than car Y. (This is our ‘t’)
  • Therefore, t (in hours) = \(\frac{1}{(S1 – S2)}\)
  • t (in minutes) = 60 × \(\frac{1}{(S1 – S2)}\)
• To find ‘t’, we just need S1 – S2 (the additional distance car X travels in 1 hour compared to car Y) ---------(*)

Statement 1
“Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour.”

Let’s find the time t in which car X shall travel an additional 1 mile more than car Y

• S1 = 50 miles/h; S2 = 40 miles/h
• S1 – S2 = 10

From (*) in the stem analysis, we can conclude that we can find ‘t’ from statement 1.

Hence, Statement 1 is sufficient.

Statement 2

“Three minutes ago, Car X was 1/2 mile ahead of Car Y.”

Three minutes ago -> Car X was 1⁄2 mile ahead of Car Y
At present-> Car X is 1 mile ahead of Car Y

• Both cars were travelling, but the gap between car X and car Y increased from 1⁄2 mile to 1 mile in the given interval.
• So, car X travelled an additional 1⁄2 mile compared to car Y in 3 minutes.
• Using unitary method again, car X will travel 2*(1/2 mile) more than car Y in 2*(3 minutes).
  
  • Hence, car X will travel 1 mile more than car Y in 6 minutes.
  • This is directly ‘t’.

Hence, Statement 2 is sufficient.

Therefore, both statements are independently sufficient, making choice D the correct answer.

Hope this helps!

Best Regards,
Ashish Arora
Quant Expert, e-GMAT