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

Bro Bunuel,

How to solve this to get the time in secs if we consider this as 2 independent PS questions?

Regards,
Sachin

ok.. i just figured out..

1)

relative speed: 10 miles/ hour = 1/6 miles / min
distance to be covered: 1 mile.

time taken : 1/(1/6) = 6 mins..

2)
find the rate :
distance : 1/2 mile
time taken: 3 mins

rate: 1/6 miles / min

now,
distance=1 mile
rate : 1/6 miles/ min

so time: 6 mins



hope it helps! ( Bunuel's statement )

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 ?

Car X is traveling at a greater speed/rate than Y.

(1) Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour.

Car X is traveling at 5/6 miles/minute.
Car Y is traveling at 4/6 miles/minute.

Every minute, Car X moves away from car Y at a rate of (5/6) - (4/6) = 1/6 miles. Therefore, car X will have moved an additional mile away from car Y in six minutes.
SUFFICIENT

(2) Three minutes ago Car X was 1/2 mile ahead of Car Y.
In three minutes, car X managed to move 1/2 mile further away from Y. Because both cars were moving at constant rates, car x would have moved away from Y at a rate of 1/6 miles per minute, or 3/6 = 1/2 miles in three minutes. We know how long it takes x to move 1/2 mile from Y and because the speed of Y is constant, the rate at which x moves away from y will be constant as well.
SUFFICIENT

(D)

Correction in the explanation.
Every minute, Car X moves away from car Y at a rate of (5/6) - (4/6) = 1/3 miles. Therefore, car X will have to travel for 6 mins to move 2 miles farther away from car Y..

Statement 1: Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.
Notice that we could easily duplicate this scenario in real life.
Start with Car X 1 mile ahead of car Y (given info)
Have Car X drive at 50 mph and car Y at 40mph.
Use a stopwatch to time how long it takes for Car X to be 2 miles ahead of Y.
As you can see, we have enough information to answer the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3 minutes ago car X was 1/2 mile ahead of car Y.
If car X is presently 1 mile ahead, we can see that car X gains 1/2 mile every 3 minutes.
At that rate, car X will gain another 1 mile in 6 minutes.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Hence D

Hey Guys,

Don't u think that there is a problem in this questions?! How do we know that the cars are moving in the same direction? If they are moving away from each other, then the answer will be completely different, since in (1) the relative speed will be 90 miles/hr, while the answer to (2) remains the same, i.e. 6 minutes.
Notice that the question does not mention that the two cars are travelling in the same direction.
What do you think?

Hello apolo

I think when we have words such as "Car A ahead of Car B" or "Car A behind of Car B" is a sign of that they are drive in the same direction.

And when cars driving in different directions there is usually wording such as: "Two cars start off at the same point on a straight highway facing opposite directions."

(1) Tells us that car X's relative speed to Y is 10 mph. With this we can easily find the time for X to increase the distance between the two cars with 1 mile. (1mile/10mph*60 minutes/hour=6 minutes)

(2) Tells us that increasing the distance 1/2 mile took 3 minutes. As the speeds in which X and Y are traveling are constant, we can conclude that X will increase the distance with an entire mile in double the time, 6 minutes.

I didn´t get why 1 is sufficient. We don´t know the directions that the cars are going. If they are at the same direction the differece rate would be 10 mph, but if they are on opposite directions, it would be 90 mph. Could anyone help me?

Why this is not E ?

The question doesn't mention anything about the direction of the cars.

Prompt analysis
Car X and car Y are travelling in the same direction.

Superset
The time could be any positive real number.

Translation
In order to find the time, we need:
1# exact value of time
2# The speed of car X and car Y
3# any relation that would help to figure the speed or time.

Statement analysis
We will use the concept of relative speed.

St 1: relative speed of car X with respect to car Y is 50-40 = 10 mph. From this reference the car X has to travel 1 mile.therefore the time taken is 1/10 hrs or 6 minutes. ANSWER

St 2: in 3 minutes, car X has travelled ½ miles, therefreo car x will travel 1 mile in 6 minutes. ANSWER

Option D

It might seem a bit silly but nowhere in the question, it was mentioned that the two cars are traveling in the opposite direction or same direction. Which according to me is relevant in deciding the answer? Bunuel, kindly let me know if I am correct or wrong?

here's a non-relative-rate approach.
remember, your goal is never to use more than 1 variable, unless absolutely necessary... and i've never seen a rate/time/distance problem that absolutely required the use of more than 1 variable.

Q: While on a straight road, car X and car Y are travelling 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 ?
^^ simplified: after how long will car X have traveled exactly 1 mile more than car Y?

(1) Car X is travelling at 50 miles per hour and car Y is travelling at 40 miles per hour.
^^ since both cars travel for exactly the same amount of time, we only need one variable.
time traveled by each car = t
--> distance traveled by car X = 50t
--> distance traveled by car Y = 40t
we want car X to travel exactly one more mile than car Y, so
50t = 40t + 1
SUFFICIENT (no reason to bother actually solving)

(2) 3 minutes ago car X was 0.5 mile ahead of car Y.
^^ this tells us that car X gains half a mile on car Y every 3 minutes.
therefore, we will need six minutes.
SUFFICIENT.

(D).

The question tells us Car X is currently 1 mile ahead of Car Y. How many minutes from now will Car X be 2 miles ahead of Car Y? Lets look at the statements:

(1) Car X is traveling at 50 miles per hour and Car Y is traveling at 40 miles per hour

From Statement 1 we know the relative speed is 50 - 40 = 10 miles per hour.

10 miles / hour = 1/6 miles/minute

1/6miles/minute = 6 minutes for Car X to be 2 miles ahead of Car Y. Statement 1 is sufficient.

(2) Three minutes ago Car X was 1/2 mile ahead of Car Y.

This statement means that in 3 minutes, Car X will be 1 mile ahead. Therefore, we can determine that in another 6 minutes, Car X will be 2 miles ahead. Statement 2 is sufficient.

Answer is D.

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.

Hi BrentGMATPrepNow, could you share your insights on this question St 2 please? I couldn't get my head around from the confusing wordings here? Thanks Brent

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 ½ 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 ½ mile to 1 mile in the given interval.
• So, car X travelled an additional ½ 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