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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # On a certain nonstop trip, Marta averaged x miles per hour for 2 hours

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Math Expert V
Joined: 02 Sep 2009
Posts: 60685
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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39 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:28) correct 29% (01:38) wrong based on 1760 sessions

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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

Kudos for a correct solution.

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4232
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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Top Contributor
7
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

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Originally posted by GMATPrepNow on 20 Sep 2016, 06:26.
Last edited by GMATPrepNow on 07 Sep 2018, 08:42, edited 1 time in total.
Manager  Joined: 26 Nov 2014
Posts: 83
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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5
6
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.
##### General Discussion
Intern  Joined: 07 Sep 2015
Posts: 5
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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3
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}

P.S. Don't forget Kudos. :D
Math Expert V
Joined: 02 Sep 2009
Posts: 60685
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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2
dave13 wrote:
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.

Bunuel, @pushpiktc chetan2u Why answer is A and not C We have two unknowns in statement one , havent we ? and when we have two unknowns and one equation how can one get answer The question asks: what is the value of (2x + 3y)/5?

Statement 1 says: 2x + 3y = 280. Could you answer the question what is the value of (2x + 3y)/5 knowing that 2x + 3y = 280?
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Intern  Joined: 15 Sep 2016
Posts: 1
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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do we not calculate total speed by sum of all distances/sum of all hours
Math Expert V
Joined: 02 Sep 2009
Posts: 60685
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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itisha wrote:
do we not calculate total speed by sum of all distances/sum of all hours

(Average Speed) = (Total Distance Covered)/(Total Time Spent)
_________________
Intern  B
Joined: 05 Jan 2015
Posts: 2
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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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)
Intern  Joined: 27 Apr 2015
Posts: 8
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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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.
VP  D
Joined: 09 Mar 2016
Posts: 1223
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.

Bunuel, @pushpiktc chetan2u Why answer is A and not C We have two unknowns in statement one , havent we ? and when we have two unknowns and one equation how can one get answer Manager  S
Joined: 15 Dec 2016
Posts: 165
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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Originally posted by jabhatta@umail.iu.edu on 29 Nov 2019, 08:55.
Last edited by jabhatta@umail.iu.edu on 29 Nov 2019, 08:57, edited 1 time in total.
Manager  S
Joined: 15 Dec 2016
Posts: 165
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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Hi Bunuel

Just out of curiosity..

If S2 had given use the actual values of x miles /hr and y miles/ hr

Could we have calculated the average speed in that case ?

I think we could have have based on the teeter totter weighted averages method

Posted from my mobile device Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours   [#permalink] 29 Nov 2019, 08:56
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