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

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Re: If Anne takes 3x seconds to run y yards, how many minutes will she tak [#permalink]
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. $$\frac{zy}{18x}$$

EG

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) $$= \frac{10z}{20y/x} = \frac{xz}{2y}$$

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Re: If Anne takes 3x seconds to run y yards, how many minutes will she tak [#permalink]
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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. $$\frac{zy}{18x}$$

EG

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

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Re: If Anne takes 3x seconds to run y yards, how many minutes will she tak [#permalink]
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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
Re: If Anne takes 3x seconds to run y yards, how many minutes will she tak [#permalink]
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