If Anne takes 3x seconds to run y yards, how many minutes will she tak

Question

If Anne takes 3x seconds to run y yards, how many minutes will she take to run 10z yards?

A.  \frac{xy}{2z}

B.  \frac{xz}{2y}

C.  \frac{10z}{3xy}

D.  \frac{z}{18xy}

E.  \frac{zy}{18x}

Source:   Experts Global GMAT  
Difficulty Level:   600

Salsanousi · Answer

First find the rate

Rate (speed) = distance/time = y/3x

Convert the 3x from seconds to minutes it will be 3x/60 = x/20

Rate = y/(x/20) = 20y/x (yards/mins)

To find the time for 10z yards

It will be time = distance/rate

10z/(20y/x) = 10xz/20y = xz/2y

Answer choice B

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KanishkM · Answer

When i see such questions, I first see which conversion is the question looking at.

Now, lets solve this question

Question speaks about minutes, So i will convert the seconds part into minutes

3x seconds to complete y yards

60 seconds(1 minute) will now take  \frac{y}{3x} * 60 yards

Now we know the work done in a minute, we can now calculate, how much time will 10 z yards take

\frac{y}{3x} * 60 will be done in 1 minute

10 z will be done in  \frac{3x}{(y*60)} *10Z

Solving that will give answer as   \frac{xz}{2y}

KarishmaB · Answer

Speed (in yards/min) = Distance (in yards)/Time (in mins)  = \frac{y}{3x/60} = \frac{20y}{x}

Time taken in mins = Distance (in yards)/Speed (in yards/min)  = \frac{10z}{20y/x} = \frac{xz}{2y}

Answer (B)

ScottTargetTestPrep · Answer

Since Anne’s rate is y/3x, it will take her 10z/(y/3x) = 30zx/y seconds or 30zx/60y = zx/2y minutes to run 10z yards.

Alternate Solution:

Let’s first convert 3x seconds to minutes: 3x/60 = x/20 minutes. Thus, it takes Anne x/20 minutes to run y yards.

Now we can set up a proportion, letting m = the number of minutes it will take her to run 10z yards. The proportion is: “x/20 minutes is to y yards as m minutes is to 10z yards”:

(x/20)/y = m/10z

Cross-multiplying, we have:

10xz/20 = my

Solving for m, we have:

10xz/20y = m

xz/2y = m

Answer: B

jfranciscocuencag · Answer

Plugging in values:

3(x) ... take 60 as x.

So 180 sec =  3 minutes .

y yards ... take  6 as yards   (because is a multiple of 3) .

This means that Anne takes   2 minutes per yard   (6yards(y)/3minutes(x))

Then, 10z ... take z as 3,  so total will be 30  ...  (because is a multiple of 6)

Solve it:   30/2   = 15 minutes.

So just look for the answer which gives you 15 (answers are given in minutes).

X = 60
Y = 6
Z = 3

B) (60)(3)/2(6) =15 minutes.

B

luisdicampo · Answer

Method 1: Algebraic Approach

First, find Anne's running rate in yards per second.
 Rate = \frac{Distance}{Time} = \frac{y}{3x}  yards/second.

Next, determine the time required to run the new distance ( 10z  yards) using this rate.
 Time_{seconds} = \frac{Distance}{Rate} = \frac{10z}{\frac{y}{3x}}

To divide by a fraction, multiply by its reciprocal:
 Time_{seconds} = 10z 	imes \frac{3x}{y} = \frac{30xz}{y}  seconds.

Crucial Step:  The question asks for the answer in  minutes , not seconds. To convert seconds to minutes, divide by 60.
 Time_{minutes} = \frac{\frac{30xz}{y}}{60}

Time_{minutes} = \frac{30xz}{60y}

Simplify the fraction by dividing numerator and denominator by 30:
 Time_{minutes} = \frac{xz}{2y}

Matches Option (B).

Method 2: Picking Numbers

Let’s choose easy numbers to work with.
Let  x = 20  (so  3x = 60  seconds, which is exactly 1 minute).
Let  y = 100  yards.
Let  z = 10  (so  10z = 100  yards).

Scenario: 
Anne takes 60 seconds (1 minute) to run 100 yards.
How many minutes does she take to run 100 yards ( 10z )?
Obviously, the answer is  1 minute .

Now, plug our chosen numbers ( x=20, y=100, z=10 ) into the options to see which one equals 1.

(A)  \frac{20 \cdot 100}{2 \cdot 10} = \frac{2000}{20} = 100  (Incorrect)
(B)  \frac{20 \cdot 10}{2 \cdot 100} = \frac{200}{200} = 1   (Correct) 
(C)  \frac{10 \cdot 10}{3 \cdot 20 \cdot 100} = 	ext{tiny fraction}  (Incorrect)

Answer: B

If Anne takes 3x seconds to run y yards, how many minutes will she tak

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If Anne takes 3x seconds to run y yards, how many minutes will she tak

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