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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?

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

This post received KUDOS

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}

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?

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

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)

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