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

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Math Expert
Joined: 02 Sep 2009
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Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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02 Sep 2015, 22:50
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Difficulty:

65% (hard)

Question Stats:

67% (02:04) correct 33% (02:24) wrong based on 302 sessions

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Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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03 Sep 2015, 02:17
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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.

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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03 Sep 2015, 09:13
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Bunuel wrote:
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Kudos for a correct solution.

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

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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03 Sep 2015, 11:35
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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

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Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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03 Sep 2015, 16:53
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Bunuel wrote:
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Kudos for a correct solution.

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

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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06 Sep 2015, 06:15
Expert's post
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Bunuel wrote:
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Kudos for a correct solution.

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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Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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19 Oct 2015, 01:26
35*(6/5 + x) = 49x

42+35x=49x

x=3, so 35*3=105

A

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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19 Oct 2015, 05:20
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Expert's post
Bunuel wrote:
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Kudos for a correct solution.

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

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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13 Aug 2016, 11:20
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.

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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22 Aug 2016, 02:06
Bunuel wrote:
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

(A) 105
(B) 120
(C) 140
(D) 147
(E) 168

Kudos for a correct solution.

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

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Re: Car X began traveling at an average speed of 35 miles per hour. After [#permalink]

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22 Sep 2017, 10:53
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Re: Car X began traveling at an average speed of 35 miles per hour. After   [#permalink] 22 Sep 2017, 10:53
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