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Math Expert V
Joined: 02 Sep 2009
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If Juan takes 11 seconds to run y yards, how many seconds  [#permalink]

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Difficulty:   5% (low)

Question Stats: 80% (00:54) correct 20% (01:09) wrong based on 941 sessions

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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

Practice Questions
Question: 38
Page: 157
Difficulty: 600

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

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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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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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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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Math Expert V
Joined: 02 Sep 2009
Posts: 55614
Re: If Juan takes 11 seconds to run y yards, how many seconds  [#permalink]

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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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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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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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1
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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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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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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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]

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Using ratios we can write:
$$\frac{11}{y}=\frac{something}{x}$$
$$Something = \frac{11x}{y}$$

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

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To travel y yard it takes 11 sec I.e
Y yard= 11 sec
1 yard= 11/Y sec
X yard= 11X/Y

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If Juan takes 11 seconds to run y yards, how many seconds  [#permalink]

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Hi All,

We're told that it takes Juan 11 seconds to run Y yards. We're asked how many seconds it takes him to run X yards at that same rate. This question can be solved by TESTing VALUES.

IF....
Y = 2
X = 4

Then Juan takes 11 seconds to run 2 yards. At that same rate, he would need 22 seconds to run 4 yards. So we're looking for an answer that = 22 when Y = 2 and X = 4...

Answer A: 11X/Y = 44/2 = 22 This IS a match
Answer B: 11Y/X = 22/4 NOT a match
Answer C: X/(11Y) = 2/44 NOT a match
Answer D: 11/(XY) = 11/8 NOT a match
Answer E: (XY)/11 = 8/11 NOT a match

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

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Top Contributor
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

Let's solve the question using the input-output approach.

For example, let's let y = 22
This means that Juan takes 11 seconds to run 22 yards, which means his speed is 2 yards per second.

From here, if we let x = 10, then the question is asking,"how many seconds will it take Juan to run 10 yards at the same rate (of 2 yards per second)?"
Well, at that speed, it will take Juan 5 seconds to run 10 yards.

In other words, if we INPUT y = 22 and x = 10, then the answer (the OUTPUT) to the question is 5.

Now we'll plug y = 22 and x = 10 into the answer choices and see which one yields the OUTPUT of 5
(A) 11x/y = (11)(10)/22 = 5 GREAT!
(B) 11y/x = (11)(22)/10 = something other than 5 ELIMINATE B
(C) x/11y = (10)/(11)(22) = something other than 5 ELIMINATE C
(D) 11/xy (11)/(10)(22) = 1/20 ELIMINATE D
(E) xy/11 = (10)(22)/(11) = 20 ELIMINATE E

Cheers,
Brent

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

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Top Contributor
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

Practice Questions
Question: 38
Page: 157
Difficulty: 600

Another option is to use equivalent ratios.

The ratio is time/distance

For every 11 seconds, Juan can run y yards
So we get the ratio 11/y

Let T = the time it takes to run x yards.
That is, For every T seconds, Juan can run x yards
We get the ratio T/x

Since Juan runs at a constant rate, we can write: we get: 11/y = T/x
Cross multiply to get: 11x = Ty
Divide both sides by y to get: 11x/y = T

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

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_________________ Re: If Juan takes 11 seconds to run y yards, how many seconds   [#permalink] 25 May 2019, 05:34
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