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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, 19:33
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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, 20:58, edited 1 time in total.
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26 Aug 2010, 20:05
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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, 22:49
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, 10:22
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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, 07:09
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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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18 Mar 2017, 02:16
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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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19 Mar 2017, 11:11
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Hi All,

While this is an older post, the prompt is still representative of the types of 'variable-heavy' prompts that you can see on the Official GMAT. This question can be solved by TESTing VALUES.

Let's TEST...
Distance to park = 6 miles
M = 2 miles per hour (driving to the park)
N = 3 miles per hour (driving from the park)
Z = 2+3 = 5 total hours driving

We're asked for the distance from the home to the park. Thus, we're looking for an answer that equals 6, when we plug in M=2, N=3 and Z=5 into the answer choices.

Answer A: 8/2 - 5/3 = 2 1/3 NOT a match
Answer B: 10/6 NOT a match
Answer C: 30/5 = 6 This IS a match
Answer D: 7/6 NOT a match
Answer E: 10/3 NOT a match

[Reveal] Spoiler:
C

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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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20 Mar 2017, 02:15
ezhilkumarank wrote:
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. $$\frac{mz}{n}$$

SHORTCUT

if m=n, time taken for 1 way will be z/2
therefore distance will be mz/2

replace n =m in the options

only option C will give the value mz/2

option C
Re: A drives at a rate of m miles per hour from his home to the   [#permalink] 20 Mar 2017, 02:15
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