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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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26 Oct 2015, 08:48
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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?
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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Updated on: 07 Sep 2018, 07:42
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Top Contributor
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?
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
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26 Oct 2015, 22:30
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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}
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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07 Nov 2016, 08:08
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)
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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18 Aug 2018, 02:08
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
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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18 Aug 2018, 02:24
2
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Expert Reply
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? _________________
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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05 May 2020, 02:15
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?
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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05 May 2020, 05:18
Expert Reply
Asad 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?
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
[#permalink]
05 May 2020, 14:28
Expert Reply
Asad 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?
When a question asks for AVERAGE SPEED over the course of an entire trip, you will almost certainly end up needing the TOTAL TIME and the TOTAL DISTANCE traveled. In this prompt, we know that the total time is 5 hours (since "Marta averaged X miles per hour for 2 HOURS and Y miles per hour for the remaining 3 HOURS"). Thus, to answer the question, we need some additional information that 'locks in' the total distance - otherwise the answer to the question will change.
At this point, total distance = 2X + 3Y
Fact 2 has no "limit" on the values of X and Y (other than the idea that X and Y must be positive, since they're speeds). With the equation Y = X + 10.... as X increases, Y will also increase... so there would be no limit to how high the total distance could become. As such, treating this as a Weighted Average isn't practical, since the total distance will just keep getting bigger and bigger as X and Y increase, so the answer to the question will change will every iteration of X and Y.
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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07 May 2020, 01:05
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Expert Reply
Asad 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?
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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25 May 2020, 12:54
The prompt is not giving to us any equalities.
We only know that Av speed= tod distance/ Tot time Tot distance is 2x+3y Tot time is 5h So the question is how much is 2x+3y/5
1) gave to use the value of 2x+3y so we can use it to find the AvSpeed. Sufficient
2) gave to us the equality y=x+10. Also if we would like to use this equality with 2x+3y/5 we will have x+6=Av Speed. Still not sufficient to have any value. So not sufficient.
Re: On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
[#permalink]
25 May 2020, 13:53
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.
Average speed = Total distance / Total time
To find the answer to this, we need to find the total distance and total time
To find total distance: Given: x mph for 2 hours (Speed = Distance/ time; hence, Distance = Speed * Time) Distance of 1st leg = 2x
Similarly y mph for 3 hours Distance of 2nd leg = 3y
Total distance = 2x + 3y
Total time = 2hr + 3 hr = 5 hr
Hence to find:
Average speed = Total distance / total time Average speed = 2x + 3y / 5.........(1)
Statement 1 2x+3y = 280
Directly substitute the value in Eq (1) 280 / 5 = 56 Hence sufficient
Statement 2 y = x + 10 Substitute the value of y in Eq (1) 2x + 3 (x +10)/5 = (5x + 30)/5 = Does not give a numeric value since we do not know the value of x... Hence not sufficient
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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours
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Updated on: 13 Dec 2020, 10:57
Top Contributor
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.
In 1 hour X miles, in 2 hours 2x miles, similarly in 1 hour y miles, 3 hours 3y miles
Average Speed \(=\frac{(Tatal \ distance)}{Total \ time}\)
\(=\frac{(2x + 3y)}{5}\)
(1) \(2x + 3y = 280\)
\( \frac{280}{5 }= 56\)
Sufficient.
(2) x+y = -10, We don't get value of 2x +3x from here.
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