Car X began traveling at an average speed of 35 miles per hour. After

These type of questions are still my biggest weakness, but I think explaining it help me... Feel free to give me feedback on my method. Please also bear with the fact that I am explaining every single step in my reasoning... Maybe it will help someone one day.

Rate * Distance = Time
Where \(T =\) time Car Y driving in Hours & \(D =\) Distance in Miles

Car X: \(35 * (T + \frac{6}{5}) = D\)
Car Y: \(49 * T = D\)

---> \(35(T + \frac{6}{5}) = 49T\)
---> \(35T + \frac{210}{5} = 49T\)
---> \(35T + 42 = 49T\)
---> \(14T = 42\)
---> \(T = \frac{42}{14} = 3\)

So we know that They both drove the same distance after Car Y had been driving for 3 hours. The question asks how far Car X had driven after this amount of time ---> \(35 * 3 = 105\) miles

Answer = A

Okay, so when car Y STARTS moving, car X has already traveled 42 miles
So, let's let t = the travel time starting when car Y STARTS moving

So, car X's TOTAL travel distance = 42 + 35t
So, car Y's TOTAL travel distance = 49t

We want the cars' travel distance to be EQUAL.
We can write: 42 + 35t = 49t
Simplify: 42 = 14t
Solve: t = 3

How many miles did car X travel from the time car Y began traveling until both cars stopped?
So, car X and car Y traveled for 3 hours (from the time car Y STARTED moving)
Car X's speed = 35 mph
So, car X's distance traveled (from the time car Y STARTED moving) = 3(35) = 105

Answer: A

Cheers,
Brent

Car X would have traveled 42 miles in 72 minutes or by the time Car Y started.
Now, Car Y has to cover 42 extra miles while running alongwith Car X.
Since Car Y covers (49 - 34 = 14) 14 additional miles each hour, it would take 3 hours to cover the same distance as Car X.
Hence, Car X would have traveled for 3 hours, thereby covering (35 X 3 = 105 miles) from the time car Y began travelling.

Therefore, A is the answer.

Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 49t
or 5t+6=7t
or t=3

Distance travelled by car X from the time car Y began traveling until both cars stopped is

35 x 3
= 105 miles

Answer:- A

Solution:

Let t be time traveled by x. So we have to subtract distance traveled in 72 min to get the answer.
So, ans = 35(t -1.2)
But, total distances traveled is same.
So,49(t-1.2) = 35t ---> 14t =49(1.2) -->t= 7(0.6)=4.2.
ans = 35(4.2-1.2) = 105

Option A

KAPLAN OFFICIAL SOLUTION:

Step 1 is to determine how far car X traveled during the 72 minutes before car Y has started. To do this, we first convert 72 minutes to 6/5 of an hour (that’s 72/60 simplified), in order to make sure our units match, as our speed is given in miles per hour. Since rate * time = distance, we know that car X traveled 35mph * 6/5 hours = 42 miles.

Step 2 we need to determine a relative rate. We do this in order to figure out how many miles car Y gains on car X each hour. To calculate this, subtract the rate of car X from the rate of car Y. 49mph – 35mph = 14mph, which is our relative rate in miles per hour, or the rate that Y gains on X per hour.

Step 3 take the distance car Y must gain on car X (that’s 42 miles, from step 1) and divide it by the number of miles car Y gains on X in an hour (that’s 14 mph from step 2) in order to find the number of hours it will take for both cars to travel the same distance: 42mi/14mph = 3 hours.

Finally, we are asked to find how far car X traveled after car Y starts. We use the time we calculated from step 3, which is 3 hours, and multiply it by car X’s rate (35mph). This gives us 3hrs * 35mph = 105 miles, which is choice (A) and the correct answer to this problem.
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35*(6/5 + x) = 49x

42+35x=49x

x=3, so 35*3=105

A

Car X travels for 72 minutes before car Y starts so the distance travelled by car X in 72 mins (i.e. 6/5 Hours) = Lead of car X over car Y = 35*(6/5) = 42 Miles

Relative Speed of Y with respect to speed of X = 49-35 = 14 miles/hour

Time taken by Y to cover the Relative Distance between X and Y in order to travel as much distance as X does = Relative Distance / Relative Speed = 42/14 = 3 hours

Distance travelled by Y in 3 hours = 49*3 = 147 miles

SO the Distance to be calculated (Travelled by X after Y started) = 147-42 = 105 miles

Answer: option A

This is a catch up question but does not easily tell us that. It says that when they both stopped they had covered the same distance from the starting point. Both cars travelling the same distance after X having left early means Y caught up. So we can apply the relative speed formula.

In my first attempt I didnt get that very clearly, so conservatively I applied another method which is below:
Car X travelled the same distance as Y when it stopped. This means
35*(t+72/60) = 49*t. This gives t = 3.
Now the question does not ask the total distance. It only wants to know how many miles did X travel after Y left. This is t*35 = 3*35 = 105.

For those that understood straight that this is a catch up problem , I will say great job decoding that! But the other method is a good one when in doubt.

By the time Car Y started to travel Car X has already traveled 42 miles. (35*6/5)
And we know that time is constant after Y started to travel : let it be T
so 35T + 42 = 49T
T = 3
So we know that Car X and Y traveled 3 hours until they have stopped.
35*3 = 105

My reasoning if it helps anyone:

Key information from the stem is both cars traveled the same distance.

Hence:

Distance of car X = distance of car Y
Distance = rate * time

35(t+72/60) = 49t
t= 3

Distance traveled by car X when car Y started is 35*3 = 105

I somehow went into the case in which both the cars are going like this X -> <- Y. But this was an easy case of catch up which means Y has to catch up with X

So After 72 minutes, car Y begins would mean that X has already traveled for 42 miles

This 42 miles will be covered by Y with Total Time = Total Distance / Total Speed
= 42 / 14
= 3 hours

Since distance is equal. This means X would have traveled Speed * time = 35 * 3 = 108 miles

A
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Car X travels for 72 mins [ 1(1/5) hrs ]
So at a speed of 35 mph, he covers 35*(6/5) = 42 miles

Now car Y has to travel 42 miles more than car X and it covers 14 miles more than car X every hour (since speed of car Y is 49 mph and that of car X is 35 mph).
Car Y will make up this distance in 42/14 = 3 hrs.

In 3 hrs, car X travels 3*35 = 105 miles

Answer (A)
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Hi GMATPrepNow,

Could you please help me with the solution of this. So i found that X travelled 42 miles during that initials head up . I am not able to continue after that

How is t equal here?

This is awsome . Thank you !

Though it's little time consuming, i follow the same framework for all problems

My reasoning is:

Time: 0 1 1.2 2 2.2 3 3.2 4 4.2

Car X 0 35 42 70 77 105 112 140 147

Car Y 0 0 0 49 98 147

Hence, after 3 hours their distances are equal. In 3 hours, X would have travelled 105 hours.

Ans A

Let t = the time car Y traveled before it stopped. Since 72 minutes = 72/60 hours = 6/5 hours, we can create the equation:

35(t + 6/5) = 49t

35t + 42 = 49t

42 = 14t

3 = t

So car X traveled 3 x 35 = 105 miles from the time car Y began travelling until both cars stopped.

Answer: A
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