PS - Rate & Times

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

Cheers,
Brent

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

Cheers,
Brent

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]

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

GMAT assassins aren't born, they're made,
Rich