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

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Math Expert
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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26 Oct 2015, 09:48
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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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Posts: 4232
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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Updated on: 07 Sep 2018, 08:42
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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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26 Oct 2015, 23:00
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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26 Oct 2015, 23:30
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
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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18 Aug 2018, 03:24
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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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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19 Sep 2016, 23:54
do we not calculate total speed by sum of all distances/sum of all hours
Math Expert
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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20 Sep 2016, 04:18
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)
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Joined: 05 Jan 2015
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Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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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)
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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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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Joined: 09 Mar 2016
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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours  [#permalink]

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18 Aug 2018, 03:08
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
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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Updated on: 29 Nov 2019, 08:57

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
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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29 Nov 2019, 08:56
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

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

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