A car and a van are traveling at different constant speeds on a straig

Question

A car and a van are traveling at different constant speeds on a straight highway. If the car is now 4 miles ahead of the van, how much time, in hours, will it take for the car to be 10 miles ahead of the van?

(1) The car is traveling 70 miles per hour and the van is traveling 65 miles per hour.

(2) One hour ago, the car was 1 mile behind the van.

EgmatQuantExpert · Answer

Solution

Given:  
• A car and a van are traveling at different constant speeds on a straight highway
• Presently the car is 4 miles ahead of the van

To find:  
• How much time the car will take to be 10 miles ahead of the van

Analysing Statement 1  
• As per the information given in Statement 1, the car is traveling at 70 mph and the truck is traveling at 65 mph
 o However, in this statement no information is provided about the movement of the van 
• Therefore, statement 1 is not sufficient to answer the question

Analysing Statement 2  
• As per the information given in Statement 2, the car was 1 mile behind the van 1 hour ago
• We also know that presently the car is 4 miles ahead of the van
 o Therefore, the car gains 5 miles in every hour, compared to the van 
• So, the time the car will take to be 10 miles ahead of the van =  \frac{10}{5}  = 2 hours
• Hence, statement 2 is sufficient to answer the question

Hence, the correct answer is option B.

Answer: B

Hero8888 · Answer

The car can not be ahead if it doesn't move in the same direction with van, otherwise you could cross the road and say that now the van is ahead of the car. Your cas would work if the author of the question mentioned East/West, Left/Right. Answer is D.

thekojoway · Answer

Statement 1 says truck instead of van. I thought the answer was D too but seeing that the speed is for a truck not a van, we still don't have any information on how fast the van was going in statement 1

push12345 · Answer

(1) The car is traveling 70 miles per hour and the van is traveling 65 miles per hour.

In this question we need to assume they are moving in same direction.
So 6 more km need to travel
So 6/(70-65)=6/5=1.2 hr
Sufficient

(2) One hour ago, the car was 1 mile behind the van.

Now car is 4 mile ahead
In 1 hour car travel 5 km
So another 6 car will take 6/5 hr=1.2 hr
Sufficient

Answer D

Give kudos if it helps

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Adityasekar · Answer

Option D is correct. 
 We don't have to solve for the answer rather we need to see if we have enough information to arrive at conclusions.

ST1 : The car is traveling 70 miles per hour and the van is traveling 65 miles per hour.  -- So the car gains 5 miles/hr over the van which provides us enough information to how much time is need approx ( 1hr 12 mins) since we need to travel 6 more miles

(2) One hour ago, the car was 1 mile behind the van.  -- This tells us that car has covered 5 Miles more in the last hour so same as ST1.

Do give kudos if you find the answer helpful.

anupam87 · Answer

Statement 1 - we get the speed of both the car and the van. Hence Sufficient 
Statement 2- Tells us that the gap is shrinking by 1 mile/hr. From this we can determine how long will it take for the car to be 10 miles ahead of the van.
Answer - D

DarleneTran · Answer

A car and a van are traveling at different constant speeds on a straight highway. If the car is now 4 miles ahead of the van, how much time, in hours, will it take for the car to be 10 miles ahead of the van?
--->We are asked to find time, so we need to know either distance or speed, or both to answer the question.

(1) The car is traveling 70 miles per hour and the van is traveling 65 miles per hour.
----->We know the speed of the car and the van, and we know how the distance changes according to the time--->We have enough data to answer the question.---->Sufficient.

(2) One hour ago, the car was 1 mile behind the van.
--->We know the correlation between time and distance, so we can probably figure out how the time will be when the car 10 miles ahead of the van--->Sufficient.

------>The answer is D.

MHIKER · Answer

Distance = Time*Speed
The car has to 6 more ahead to total 10 miles

(1) Car goes 5 miles ahead of the van in 1 hour., For 6 mile the car will take=6/5=1.2 hours; Sufficient.

(2) So, the car traveled 4 miles and 1 mile =5 miles one hour, the For 6 mile the car will take=6/5=1.2 hours: Sufficient

The answer is D

dave13 · Answer

hey Hero8888 why are you equating times ? do you mean that whn car is 10 miles ahead their times are equal ? shouldnt we equate times only in cases when vehicles can meet each other or cross some point together ... a bit confused

maybe you chetan2u can explain why

chetan2u · Answer

The e-gmat solution believes we do not know the ways these vehicles are moving, so it could be they are moving in opposite directions too, then 4 miles will become 10 miles in a very short period => the combined speed will be 70+65=135, so 6 miles will be covered in 6/135.
However Hero8888 believes that the vehicles are moving in the same direction, and that is the only possibility => Relative speed = 70-65=5, so 6 miles in 6/5 or 1.2 hr

Yes, both the above points would be correct if we were told the DISTANCE between the two is 4 miles, and when will it become 10 miles. Here the vehicles could be moving in opposite or same directions and in each case, the answer will be different.
But here it is given that car is AHEAD of van by 4 miles. This does mean in a way that both are travelling in the same direction and so A is also sufficient, and Hero888 is correct.

In actual GMAT, the question may be worded differently.

dave13 · Answer

thanks chetan2u i understood that cars are moving in same direction, but what i didnt get is why are we equating times ? see attached solution by hero8888 .

so as far as i know we can equate times when objects meet each other or they cross some point at same time .... because under these conditions times of vehicles will be equal

hello BrentGMATPrepNow, Happy New Year

perhaps you can explain

chetan is on winter new year holidays, skiing in swiss alps

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perhaps you can explain

chetan is on winter new year holidays, skiing in swiss alps

BrentGMATPrepNow · Answer

Given : A car and a van are traveling at different constant speeds on a straight highway. The car is now 4 miles ahead of the van

Target question :    How much time, in hours, will it take for the car to be 10 miles ahead of the van?

Statement 1 : The car is traveling 70 miles per hour and the van is traveling 65 miles per hour.  
We don't really need to do any math here. 
We need only recognize that we COULD duplicate this scenario in real life. That is, we could start with a car 4 miles ahead of a van. Then, both vehicles could start driving their respective speeds (70 miles per hour and 65 miles per hour), at which point we could easily time  how long it takes for the car to be 10 miles ahead of the van . 
So, Statement 1 is sufficient

Here's a more mathematical approach....
Statement 1 tells us that, after 1 hour has elapsed, the car has travelled 70 miles and the van has travelled 65 miles. 
In other words, each hour, the car travels  5  miles further than the van. 
In order for the car to be 10 miles ahead of the van, it must travel  6  miles more than the van (since the car is starting 4 miles ahead of the van)

Time = distance/rate =  6 / 5  =  1 1/5 hours 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : One hour ago, the car was 1 mile behind the van 
We already know that the car is PRESENTLY 4 miles ahead of the van
So, statement 2 is indirectly telling us that, for each hour, the car travels  5  miles further than the van. 
In order for the car to be 10 miles ahead of the van, it must travel  6  miles more than the van (since the car is starting 4 miles ahead of the van)

Time = distance/rate =  6 / 5  =  1 1/5 hours 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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A car and a van are traveling at different constant speeds on a straig

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