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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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New post Updated on: 19 Apr 2012, 19:58
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Question Stats:

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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. \(\frac{mz}{n}\)

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Originally posted by ezhilkumarank on 26 Aug 2010, 18:33.
Last edited by Bunuel on 19 Apr 2012, 19:58, edited 1 time in total.
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Re: Rate --- GMAT Practice Question.  [#permalink]

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New post 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 \(\frac{d}{m}+\frac{d}{n}=z\) --> \(d(\frac{m+n}{mn})=z\) --> \(d=\frac{mnz}{m+n}\).

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

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New post 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 \(\frac{d}{m}+\frac{d}{n}=z\) --> \(d(\frac{m+n}{mn})=z\) --> \(d=\frac{mnz}{m+n}\).

Answer: C.


Bunuel -- you made it look so simple. I could not get my mind cranked up so quickly. Guess I have to practice more. :-D
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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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New post 19 Mar 2017, 10:11
1
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

Final Answer:

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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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New post 20 Mar 2017, 01:15
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
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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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New post 18 Aug 2018, 19:07
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. \(\frac{mz}{n}\)


Let the distance between home and park be d. Driving from home to the park, the driver spends d/m hours, and, driving from the park to home, the driver spends d/n hours. Since we are given that the total time spent is z, we can create the following equation:

d/m + d/n = z

Let’s multiply each side by mn:

dn + dm = mnz

d(n + m) = mnz

d = mnz/(n + m)

Answer: C
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Re: A drives at a rate of m miles per hour from his home to the &nbs [#permalink] 18 Aug 2018, 19:07
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