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# A drives at a rate of m miles per hour from his home to the

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A drives at a rate of m miles per hour from his home to the [#permalink]

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26 Aug 2010, 18:33
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82% (02:47) correct 18% (02:46) wrong based on 182 sessions

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A drives at a rate of m miles per hour from his home to the park. On his return trip he drives at a rate of n miles per hour. How far away from his home is the part if he spends a total of z hours in the car, making no stops along the way?

A. $$\frac{n+z}{m}-\frac{z}{n}$$

B. $$\frac{m+n+z}{mn}$$

C. $$\frac{mnz}{m+n}$$

D. $$\frac{m+z}{mn}$$

E. $$\frac{mz}{n}$$
[Reveal] Spoiler: OA

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Last edited by Bunuel on 19 Apr 2012, 19:58, edited 1 time in total.
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26 Aug 2010, 19:05
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ezhilkumarank wrote:
Question: A drives at a rate of m miles per hour from his home to the park. On his return trip he drives at a rate of n miles per hour. How far away from his home is the part if he spends a total of z hours in the car, making no stops along the way?

A) $$((n+z)/m) - (z/n)$$
B) $$(m+n+z)/mn$$
C) $$(mnz)/(m+n)$$
D) $$(m+z)/mn$$
E) $$mz/n$$

Let the distance between home and park be $$d$$.

From home to park A would need $$\frac{d}{m}$$ hours and from park to home A would need $$\frac{d}{n}$$ hours as A spent total of z hours for round trip then $$\frac{d}{m}+\frac{d}{n}=z$$ --> $$d(\frac{m+n}{mn})=z$$ --> $$d=\frac{mnz}{m+n}$$.

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Re: Rate --- GMAT Practice Question. [#permalink]

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26 Aug 2010, 21:49
Bunuel wrote:
ezhilkumarank wrote:
Question: A drives at a rate of m miles per hour from his home to the park. On his return trip he drives at a rate of n miles per hour. How far away from his home is the part if he spends a total of z hours in the car, making no stops along the way?

A) $$((n+z)/m) - (z/n)$$
B) $$(m+n+z)/mn$$
C) $$(mnz)/(m+n)$$
D) $$(m+z)/mn$$
E) $$mz/n$$

Let the distance between home and park be $$d$$.

From home to park A would need $$\frac{d}{m}$$ hours and from park to home A would need $$\frac{d}{n}$$ hours as A spent total of z hours for round trip then $$\frac{d}{m}+\frac{d}{n}=z$$ --> $$d(\frac{m+n}{mn})=z$$ --> $$d=\frac{mnz}{m+n}$$.

Bunuel -- you made it look so simple. I could not get my mind cranked up so quickly. Guess I have to practice more.
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Re: A drives at a rate of m miles per hour from his home to the [#permalink]

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30 Jun 2014, 09:22
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Re: A drives at a rate of m miles per hour from his home to the [#permalink]

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01 Sep 2015, 06:09
Hello from the GMAT Club BumpBot!

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