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Frederique traveled x/8 of the total distance of a trip

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Manager
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Joined: 17 Nov 2013
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Frederique traveled x/8 of the total distance of a trip [#permalink]

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New post 29 Sep 2016, 17:37
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this question comes from Prep4Gmat app

Frederique traveled x/8 of the total distance of a trip at an average speed of 40 miles per hour, where 1=<x=<7. She traveled the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Frederique's average speed for the entire trip?

A) (180-x)/2
B) (x+60)/4
C) (300-x)/8
D) 800/(120+x)
E) 960/(x+16)
[Reveal] Spoiler: OA
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Re: Frederique traveled x/8 of the total distance of a trip [#permalink]

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New post 30 Sep 2016, 10:19
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lalania1 wrote:
this question comes from Prep4Gmat app

Frederique traveled x/8 of the total distance of a trip at an average speed of 40 miles per hour, where 1=<x=<7. She traveled the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Frederique's average speed for the entire trip?

A) (180-x)/2
B) (x+60)/4
C) (300-x)/8
D) 800/(120+x)
E) 960/(x+16)

Dear lalania1,

I'm happy to respond. :-)

Here's a blog you might find germane:
GMAT Distance and Work: Rate Formula

Here's my solution.

There are two legs in the trip. Call the total distance D. In the first leg, she covers a distance of D*(x/8) at a speed of 40 mph, and in the second leg, she covers a distance of D*((8 - x)/8) at a speed of 60 mph.

We need to calculate the time in each leg. Since D = RT, we know that T = D/R.

\(T_1 = \frac{x}{8}*D \div 40 = \frac{xD}{8*40}\)

\(T_2 = \frac{(8-x)}{8}*D \div 60 = \frac{(8-x)D}{8*60}\)

Leave the denominators unmultiplied for the moment.

\(T_{total} = T_1 + T_2 = \frac{xD}{8*40} + \frac{(8-x)D}{8*60}\)

\(T_{total} = \frac{3xD}{8*120} + \frac{2(8-x)D}{8*120}\)

\(T_{total} = \frac{(16 + x)D}{8*120} = \frac{(16 + x)D}{960}\)

Now, to find the average velocity, divide the total distance D by the total time.

\(v_{average} = \frac{D}{T_{total}} = D \times \frac{960}{(16 + x)D} = \frac{960}{(16 + x)}\)

Answer = (E)

Does all this make sense?

Mike :-)
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Mike McGarry
Magoosh Test Prep

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Concentration: Operations, General Management
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Re: Frederique traveled x/8 of the total distance of a trip [#permalink]

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New post 30 Sep 2016, 11:44
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Hi,

I used 'plugging in' approach to solve this.

Let total distance is 200 miles and X=4.

So, half(4/8) of the distance i.e. 100 miles was traveled at 40 mph and rest 100 at 60 mph.

Thus, the average speed will be (2*40*60)/(40+60)=48.

Now plugging in the value of x in the answer choices, we get E as 48.

Regards,

Amulya
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Re: Frederique traveled x/8 of the total distance of a trip [#permalink]

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New post 01 Oct 2016, 09:57
I think for me it is easier to use smart numbers

Step1: smart numbers d=200 and x=4. Why? well they are easy to use. I could have used d=240 too to keep it easier but I wanted to use the same numbers that a prior user did so to compare and contrast.
step2: identify what the question is asking. the question is asking the Rt, so that is Rt= Dt/Tt. it also asks to provide the answer in terms of x, so that means that at the very end I will have to use x=4 to plug and find the Rt that I get in my execution part.
step3: solve for R(t)

R T = D
40 t1 = (4/8) 200 => t1 = 5/2
60 t2 = (4/8) 200 => t2 = 5/3

R(t) T(t) = D(t)
R(t) = D(t)/T(t) = 200/(5/2 + 5/3) = 48

Step4: refresh your memory, so you are using x=4 replace it into the answers to find out which one gives 48. => 960/(4+16) => 960/20 = 48. Answer E is the correct answer.
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Re: Frederique traveled x/8 of the total distance of a trip [#permalink]

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New post 27 Feb 2017, 02:58
if x =8, average speed will come 40 and if x =0 average speed will come 60. Checking the options we get option E as answer.
Re: Frederique traveled x/8 of the total distance of a trip   [#permalink] 27 Feb 2017, 02:58
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Frederique traveled x/8 of the total distance of a trip

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