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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours

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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?

(1) 2x + 3y = 280
(2) y = x + 10

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[Reveal] Spoiler: OA

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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Average speed = Total distance/Total time ;
Total distance = Avg speed * Total time

Marta averaged x miles per hour for 2 hours = 2x
y miles per hour for the remaining 3 hours = 3y
Total distance = 2x+3y

Total time = 2+3 = 5 hrs

Avg speed = 2x+3y/5

St 1: 2x+3y=280

Avg speed = 280/5 = 56m/h. Sufficient.

St 2: y = x + 10, Not sufficient.

Ans A.

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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An easy question.
The average speed can be taken out by adding Marta's speed per hour for each hour divided by the total no of hours she traveled. So, we are given that she travels with x miles per hour for 2 hours and y miles per hour for 3 hours, hence average speed would be = (2x+3y)/5.

Statement 1. 2x+3y=280, which can be written as (2x+3y)/5=56. {Sufficient}
Statement 2. y = x+10, 2 variables 1 eqn {Insufficient}

Answer: A

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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New post 19 Sep 2016, 23:54
do we not calculate total speed by sum of all distances/sum of all hours

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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Bunuel wrote:
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?

(1) 2x + 3y = 280
(2) y = x + 10

Kudos for a correct solution.


Target question: What was Marta's average speed for the entire trip?

This is a great candidate for rephrasing the target question.
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Given: Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours
Average speed = (total distance)/(total time)
- Travelling at x miles per hour for 2 hours, Marta travels 2x miles
- Travelling at y miles per hour for 3 hours, Marta travels 3y miles
So, her average speed = (2x + 3y)/(2 hours + 3 hours)
= (2x + 3y)/5
So, we can REPHRASE our target question....
REPHRASED target question: What is the value of (2x + 3y)/5?

Statement 1: 2x + 3y = 280
This looks VERY SIMILAR to our REPHRASED target question.
If we divide both sides by 5, we get: (2x + 3y)/5 = 56
Perfect!! Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = x + 10
This information cannot help us determine the value of (2x + 3y)/5.
Here's why:
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 5 and y = 15. In this case (2x + 3y)/5 = [2(5) + 3(15)]/5 = 11
Case b: x = 10 and y = 20. In this case (2x + 3y)/5 = [2(10) + 3(20)]/5 = 16
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer =
[Reveal] Spoiler:
A


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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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New post 07 Nov 2016, 09:08
How are you guys coming up with 2x and 3y. I see everyone skipping the step. please show the algebra to come up with 2x + 3y and please show the unit Hours (H)

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours [#permalink]

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New post 03 Oct 2017, 18:20
We are looking for total distance divided by total time

We are told that Marta averaged X mph for 2 hours and Y mph for 3 hours. We know the total time is 5 hours. The distance, the numerator, is:

X(miles/hours)*2hours + Y(miles/hours)*3hours

The hours cancel and you have 2x miles + 3y miles for the numerator.

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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours   [#permalink] 03 Oct 2017, 18:20
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