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PS - Rate & Times

by bml1105 » Sun May 04, 2014 5:23 pm
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
Correct Answer: A
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by Brent@GMATPrepNow » Sun May 04, 2014 5:35 pm
bml1105 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
One 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
So, the answer is A

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Brent
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by Brent@GMATPrepNow » Sun May 04, 2014 5:40 pm
bml1105 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
Another approach is to use the various speed-distance-time formulas.

Juan takes 11 seconds to run y yards
Speed = distance/time
So, Juan's speed= y/11 yards per second

How many seconds will it take him to run x yards at the same rate
Time = distance/speed
So, Time = x/(y/11)
= 11x/y
= A

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Brent
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by Brent@GMATPrepNow » Sun May 04, 2014 5:49 pm
bml1105 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
We can also 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

A is the only answer that works.

Cheers,
Brent[/spoiler]
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by bml1105 » Sun May 04, 2014 6:25 pm
I was using the formula of Rate X Time = Distance

Rate = 11/y
Time = what we're trying to find
Distance = x

x/(11/y) = x(y/11) = xy/11

How come that doesn't work?
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by [email protected] » Sun May 04, 2014 7:35 pm
Hi bml1105,

There's one small mistake in your approach:

To use the Distance Formula, the Rate has to be in the form "distance/time" (e.g.. miles per hour).

In this prompt, the rate is inverted (it states "11 seconds to run Y yards"; that's "time/distance")

Converting the rate to the correct format gives us....

Rate = Y/11
Distance = X
Time = T

D = R(T)

X = (Y/11)T

X/(Y/11) = T

11X/Y = T

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by bml1105 » Mon May 05, 2014 6:16 am
Thanks Rich! I woke up this morning and realized what I had done wrong. Dreaming about GMAT problems cannot be a good sign!
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