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

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. \(\frac{n+z}{m}-\frac{z}{n}\)

B. \(\frac{m+n+z}{mn}\)

C. \(\frac{mnz}{m+n}\)

D. \(\frac{m+z}{mn}\)

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

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}

Bunuel · Accepted Answer

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.

ezhilkumarank · Answer

Bunuel -- you made it look so simple. I could not get my mind cranked up so quickly. Guess I have to practice more. :-D

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made,
Rich

KrishnakumarKA1 · Answer

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

JeffTargetTestPrep · Answer

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

TheUltimateWinner · Answer

When can we ADD or SUBTRACT things in the real world? 
------> ONLY when BOTH have EXACTLY THE SAME UNITS.

REMEMBER:  
 NEVER pick an answer choice that's absurd in the real world!

Here the question is asking about MILES (distance).
From the question,
m,n=SPEEDS in MILES/HOUR
z=TIME in HOUR
 Considering only Numerator part:

A)   n+z  ------>  \frac{miles}{hour}+hour 
Again, we're mistakenly adding 2 DIFFERENT units! So, out.

B)   m+n+z  ----->  \frac{miles}{hour}+\frac{miles}{hour}+hour 
Again, we can't add TIME with SPEED. So, bye.

D)   m+z  ---->  \frac{miles}{hour}+hour 
We're mistakenly adding TIME with SPEED. So, out.

We're eliminating A,B, and D, because they don't make sense in real life.

Now, considering both Denominator and Numerator: 
 E)   \frac{mz}{n}  ----->  \frac{miles}{hour}/\frac{miles}{hour} × hour 
--->  hour  (this is NOT our goal; our goal is MILES). So, out.

C)   \frac{mnz}{m+n}  ------> Considering "denominator" 
 ------>  Considering Denominator : equation (1)
 m+n  ---->  \frac{miles}{hour}  +  \frac{miles}{hour}  gives the unit  \frac{miles}{hour}

------>  Considering Numerator : equation (2)
 mnz  ---->  \frac{miles}{hour}  ×  \frac{miles}{hour}  × hour

Dividing equation (2) by equation (1): We get   miles  
---> This is our goal.

bumpbot · Answer

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