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On his tirp form Alba to Benton, Julio dorve the first x

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On his tirp form Alba to Benton, Julio dorve the first x  [#permalink]

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New post 18 Aug 2010, 21:33
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Hey everyone,

Here's a DS Gmat prep question that had me stumped. I'd appreciate some good explanations. Thanks!

On his tirp form Alba to Benton, Julio dorve the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first x miles?

(1) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
(2) On this trip, it took Julio 4 more hours has drive the first x miles than to drive the remaining distance

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-his-trip-from-alba-to-benton-julio-drove-the-first-x-104762.html

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Re: On his tirp form Alba to Benton, Julio dorve the first x  [#permalink]

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New post 18 Aug 2010, 21:56
A, since by below calculation you can derive the answer -

x/50 + (530-x)/60 = 10

this comes to 350 km

But just by saying first x km took 4 hours more will not solve the purpose, hope i am right and clear
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Re: On his tirp form Alba to Benton, Julio dorve the first x  [#permalink]

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New post 18 Aug 2010, 22:00
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Let the distance between Alba and Benton be 'k'. So, Julio drove the first 'x' miles at a rate of 50 miles per hour and the remaining 'k-x' at a rate of 60 miles per hour. You have to find out the value of x/50.

Statement 1 tells you that x/50 + (k-x)/60 = 10 and k = 530. Using this information you get that x/50 + (530-x)/60 = 10 and you can solve for x (=350). So, x/50 = 350/50 = 7 hours. Sufficient.

Statement 2 tells you that (k-x)/60 - x/50 = 4. You cannot solve for x unless you know the value of k in this statement. So it is insufficient.

So, the answer is A.
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Re: On his tirp form Alba to Benton, Julio dorve the first x  [#permalink]

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New post 13 Nov 2011, 02:50
On his trip from Alba to Bento, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour, how long did it take Julio to drive the x miles?

(1) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
(2) On this trip, it took Julio 4 more hour to drive the first x miles than to drive the remaining distance.

As the OA was again not provided this is how I solved it. Can someone be please kind enough to let me know whether I am right or wrong?

Here is how I solved it:

Let's say:

Total Distance - D
Time required to travel x miles - T1
Time required to travel D-x miles - T2
Rate to travel x miles - 50mph
R=D/T => 50=x/T1 and therefore x = 50*T1 ----------------------------------------------(1)

R=D/T => 60=D-x/T2 and therefore x = D-60*T2 ------------------------------------------(2)

So now the question becomes what is T1?

Considering Statement 1

T1+T2=10
T2=10-T1 -------------------------------------------------------------------------------(3)
D = 530

Substituting the value of D in equation 2 above

x = 530-60*T2

Considering the total distance is D, we can say Equation 1 is equal to Equation 2 i.e.
50*T1 = 530-60*T2 ----------------------------------------------------------------------(4)

Substituting the value of T2 from equation 3 to equation 4 will give me the value of T1 and therefore is sufficient to answer the question.

Considering Statement 2

Speed to cover first x miles = 50 mph
Let T1 be the time required to cover x miles & D be the total distance

As R=D/T, we know x/T1+4=50 ------------------------(1)
x-D/T1= 60 ------------------------(2)

2 equations and 3 variables therefore insufficient.

Therefore, statement 1 alone is sufficient to answer this question.
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Re: On his tirp form Alba to Benton, Julio dorve the first x  [#permalink]

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New post 13 Nov 2011, 03:30
Your approach as well as the answer is correct i.e. Statement 1 alone is sufficient to answer this question.

However, I could spot a minor error in your equations for the Statement 2.


You have assumed T1 to be the time required to cover x miles & D to be the total distance

Therefore, equation 1 should be x/T1 = 50 and not x/T1+4=50

Similarly, equation 2 will be (D-x)/(T1-4) = 60 and not x-D/T1 = 60
This is because you have assumed time T1 for the first x miles which is 4 hours more than the time for the remaining distance. Hence the time required to travel the remaining distance should be T1-4 hours i.e. 4 hours less than the previous time required to travel x miles.

Hope this helps. :)

Cheers!
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Re: On his tirp form Alba to Benton, Julio dorve the first x  [#permalink]

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New post 14 Aug 2017, 05:29
On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first X miles?

(1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles --> \(total \ time=10=\frac{x}{50}+\frac{530-x}{60}\) --> we have the linear equation with one unknown, so we can solve for \(x\). Sufficient.

(2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance --> \(\frac{x}{50}=\frac{y}{60}+4\), where \(y\) is the remaining distance --> we have the linear equation with two unknowns, so we can not solve for \(x\). Not sufficient.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-his-trip-from-alba-to-benton-julio-drove-the-first-x-104762.html

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Re: On his tirp form Alba to Benton, Julio dorve the first x &nbs [#permalink] 14 Aug 2017, 05:29
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