If Juan takes 11 seconds to run y yards, how many seconds : GMAT Problem Solving (PS)
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# If Juan takes 11 seconds to run y yards, how many seconds

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If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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11 Sep 2012, 03:40
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If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

(A) 11x/y
(B) 11y/x
(C) x/(11y)
(D) 11/(xy)
(E) xy/11

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Question: 38
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Difficulty: 600
[Reveal] Spoiler: OA

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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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11 Sep 2012, 03:40
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SOLUTION

If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

(A) 11x/y
(B) 11y/x
(C) x/(11y)
(D) 11/(xy)
(E) xy/11

Rate*Time=Distance.

Since, Juan takes 11 seconds to run $$y$$ yards, then his rate is $$Rate=\frac{Distance}{Time}=\frac{y}{11}$$ yards per second.

To run $$x$$ yards at this rate he'll need $$Time=\frac{Distance}{Rate}=\frac{x}{(\frac{y}{11})}=\frac{11x}{y}$$.

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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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11 Sep 2012, 08:32
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

(A) 11x/y
(B) 11y/x
(C) x/(11y)
(D) 11/(xy)
(E) xy/11

y yards ---------------------------- 11 secs (1)
1 yard ----------------------------- 11/y secs (2)
x yards ---------------------------- 11x/y secs (3)

To crosscheck, (3) can be made (1) by cross-multiplying both sides.

Hence, A
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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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12 Sep 2012, 12:55
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

(A) 11x/y
(B) 11y/x
(C) x/(11y)
(D) 11/(xy)
(E) xy/11

Practice Questions
Question: 38
Page: 157
Difficulty: 600

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Since t = 11 seconds represents time, one can immediately eliminate answers C,D and E, because they don't have units of time.
(C) x/(ty) has units of 1/time
(D) t/(xy) has units of time/speed squared, which finally is time cubed/distance squared
(E) xy/t has units of speed squared/time, which finally is distance squared/time cubed

To choose between (A) and (B), we should keep in mind that time is distance/speed. Since the distance in our case is x, it should appear in the numerator.

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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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14 Sep 2012, 04:41
SOLUTION

If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

(A) 11x/y
(B) 11y/x
(C) x/(11y)
(D) 11/(xy)
(E) xy/11

Rate*Time=Distance.

Since, Juan takes 11 seconds to run $$y$$ yards, then his rate is $$Rate=\frac{Distance}{Time}=\frac{y}{11}$$ yards per second.

To run $$x$$ yards at this rate he'll need $$Time=\frac{Distance}{Rate}=\frac{x}{(\frac{y}{11})}=\frac{11x}{y}$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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14 Sep 2012, 23:47
y yard s for 11 second
x yards for 11x/y second
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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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25 Jan 2014, 18:09
If you don't want to do fancy calculations you can just pick numbers...

y = 1
x = 2

And the questions re-phrased would be:

If Juan takes 11 seconds to run 1 yards, how many seconds will it take him to run 2 yards at the same rate?

It will take him 22 seconds to run 2 yards. Now just use those x and y values in the answers and find the one that equals 22 (which is B).
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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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23 Oct 2014, 02:02
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y yards-------------- 11 seconds
x yards ------------- ? seconds

(11*x)/y seconds
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If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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15 Jan 2015, 04:58
This was an easy one, but I do have a questions concerning rates.

When is it that we HAVE to find the rate at which 1 unit of work is done, in order to calculate another rate?

I hope my question is understandable...

Thank you,
Natalia
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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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14 Feb 2015, 09:47
pacifist85 wrote:
This was an easy one, but I do have a questions concerning rates.

When is it that we HAVE to find the rate at which 1 unit of work is done, in order to calculate another rate?

I hope my question is understandable...

Thank you,
Natalia

If you construct a table which is like the one given below it will be clear to you what you have been given and what you need to find out what is asked. For this question,
R * T = D
? * 11 = y

and we need to find out

R * T = D
? * ? = x
you need the rate here to find out the time.That as specified by the question is the same as the first case. So R=y/11.
So time=x/(y/11)=11x/y.

Kudos please if this helped anyhow.
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Re: If Juan takes 11 seconds to run y yards, how many seconds [#permalink]

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27 May 2016, 06:18
Bunuel wrote:
If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

(A) 11x/y
(B) 11y/x
(C) x/(11y)
(D) 11/(xy)
(E) xy/11

This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.

Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.

We can find Juan’s rate as follows: Rate = Distance/Time = y yards/11 seconds

Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:

Time = Distance/Rate

Time = x yards/(y yards/11 seconds)

Time = (x yards) x (11 seconds/y yards)

Time = 11x/y seconds

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Re: If Juan takes 11 seconds to run y yards, how many seconds   [#permalink] 27 May 2016, 06:18
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