GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Aug 2020, 06:26 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Jacob drove from Town A to Town B at an average rate of x miles per ho

Author Message
TAGS:

### Hide Tags

Senior Manager  B
Joined: 15 Oct 2015
Posts: 312
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)
Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

26 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:02) correct 34% (01:58) wrong based on 530 sessions

### HideShow timer Statistics

Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?

$$\frac{(x+y+z)}{3}$$

$$\frac{3xyz}{(xy+yz+zx)}$$

$$\frac{xyz}{(x+y+z)}$$

$$\frac{(xy+yz+zx)}{(x+y+z)}$$

$$\frac{3(x+y+z)}{xyz}$$
SVP  B
Joined: 06 Nov 2014
Posts: 1856
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

5
5
Nez wrote:
Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?

$$\frac{(x+y+z)}{3}$$

$$\frac{3xyz}{(xy+yz+zx)}$$

$$\frac{xyz}{(x+y+z)}$$

$$\frac{(xy+yz+zx)}{(x+y+z)}$$

$$\frac{3(x+y+z)}{xyz}$$

The best way to go about in these question is to find out the total distance covered and the total time taken.

Assume the distance for one trip = d
Total distance covered = 3d.
Time take for 1st trip = d/x
Time take for 2nd trip = d/y
Time take for 3rd trip = d/z

Average speed = total distance/ total time

Average speed = 3d/ (d/x + d/y + d/z) = 3 / (1/x + 1/y + 1/z) = 3xyz / (yz + zx + xy)
Option B
##### General Discussion
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4985
GMAT 1: 770 Q49 V46
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

2
3
Nez wrote:
Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?

$$\frac{(x+y+z)}{3}$$

$$\frac{3xyz}{(xy+yz+zx)}$$

$$\frac{xyz}{(x+y+z)}$$

$$\frac{(xy+yz+zx)}{(x+y+z)}$$

$$\frac{3(x+y+z)}{xyz}$$

Average speed = (total distance traveled)/(total travel time)
= (total distance)/(time of 1st journey + time of 2nd journey + time of 3rd journey)

Let d = the distance between Town A and Town B
So, total distance traveled = 3d

Time = distance/speed
time of 1st journey = d/x
time of 2nd journey = d/y
time of 3rd journey = d/z

Total time = d/x + d/y + dz
To simplify, rewrite with common denominator: dyz/xyz + dxz/xyz + dxy/xyz
So, total time = (dyz + dxz + dxy)/xyz

Average speed = (total distance)/(total time)
= 3d/[(dyz + dxz + dxy)/xyz]
= (3dxyz)/(dyz + dxz + dxy)
Divide top and bottom by d to get: (3xyz)/(yz + xz + xy)

Cheers,
Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course. Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

2
Nez wrote:
Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?

$$\frac{(x+y+z)}{3}$$

$$\frac{3xyz}{(xy+yz+zx)}$$

$$\frac{xyz}{(x+y+z)}$$

$$\frac{(xy+yz+zx)}{(x+y+z)}$$

$$\frac{3(x+y+z)}{xyz}$$

For this and other formulas, check: http://www.veritasprep.com/blog/2015/02 ... -the-gmat/
_________________
Karishma
Veritas Prep GMAT Instructor

VP  D
Joined: 07 Dec 2014
Posts: 1260
Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

Nezdem wrote:
Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?

$$\frac{(x+y+z)}{3}$$

$$\frac{3xyz}{(xy+yz+zx)}$$

$$\frac{xyz}{(x+y+z)}$$

$$\frac{(xy+yz+zx)}{(x+y+z)}$$

$$\frac{3(x+y+z)}{xyz}$$

3/[(1/x)+(1/y)+(1/z)]➡
3/[(xy+yz+zx)/xyz]➡
3xyz/(xy+yz+zx)
B
Board of Directors P
Joined: 17 Jul 2014
Posts: 2420
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

pretty time consuming...
we have the same distance.
say D.
time taken for first leg: D/x
time taken for second leg: D/y
time taken for third leg: D/z
total time: D/x + D/y + D/z => after re-arranging - we get: D(yz+xz+xy)/xyz
total distance: 3D.
3D divide by D(yz+xz+xy)/xyz
we get:
3xyz/(yz+xz+xy)
Manager  G
Joined: 22 Nov 2016
Posts: 245
Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

Also use some simple values. x=1, y=2, z=3. Let distance d = 6.
$$Avg speed = \frac{total distance}{total time}$$
= $$\frac{6*3}{(6+3+2)} = \frac{18}{11}$$

Plugging in values for x,y,z and d

1) $$\frac{x+y+z}{3} = \frac{6}{3} = 2$$......... wrong
2) $$\frac{3xyz}{(xy+yz+zx)} = \frac{18}{11}$$...............correct

Originally posted by sasyaharry on 02 Jul 2017, 14:10.
Last edited by sasyaharry on 03 Jul 2017, 07:43, edited 1 time in total.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 4002
Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

sasyaharry wrote:
Also use some simple values. x=1, y=2, z=3. Let distance d = 6.
$$Avg speed = \frac{total distance}{total time}$$
= $$\frac{6*3}{(6+3+2)} = \frac{9}{5}$$

Plugging in values for x,y,z and d

1) $$\frac{x+y+z}{3} = \frac{6}{3} = 2$$......... wrong
2) $$\frac{3xyz}{(xy+yz+zx)} = \frac{9}{5}$$...............correct

Your fraction should be $$\frac{18}{11}$$, not $$\frac{9}{5}$$. With your numbers for d, x, y, and z, answer B does indeed yield the correct answer. Cheers!
_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.

BLACK LIVES MATTER.
Manager  G
Joined: 22 Nov 2016
Posts: 245
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

genxer123 wrote:
sasyaharry wrote:
Also use some simple values. x=1, y=2, z=3. Let distance d = 6.
$$Avg speed = \frac{total distance}{total time}$$
= $$\frac{6*3}{(6+3+2)} = \frac{9}{5}$$

Plugging in values for x,y,z and d

1) $$\frac{x+y+z}{3} = \frac{6}{3} = 2$$......... wrong
2) $$\frac{3xyz}{(xy+yz+zx)} = \frac{9}{5}$$...............correct

Your fraction should be $$\frac{18}{11}$$, not $$\frac{9}{5}$$. With your numbers for d, x, y, and z, answer B does indeed yield the correct answer. Cheers!

gracias. Corrected.
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

Ekland wrote:
Jacob drove from Town A to Town B at an average rate of x miles per hour, then returned along the same route at y miles per hour. If he then drove back to Town B at z miles per hour along the same route, what was Jacob’s average rate of speed for the entire trip, in miles per hour?

$$\frac{(x+y+z)}{3}$$

$$\frac{3xyz}{(xy+yz+zx)}$$

$$\frac{xyz}{(x+y+z)}$$

$$\frac{(xy+yz+zx)}{(x+y+z)}$$

$$\frac{3(x+y+z)}{xyz}$$

To solve, we can use the formula for average rate:

average rate = total distance/total time

We can let distance from Town A to Town B (or vice versa) = d, and since he went from A to B, then from B to A, and then from A to B, his total distance traveled was 3d. Recall that time = distance/rate, so the time to get from Town A to Town B = d/x, the time it takes to get from Town B back to Town A = d/y, and the time it takes to go back to Town B = d/z. Thus:

average rate = 3d/(d/x + d/y + d/z)

To combine the three fractions in the denominator, we use the common denominator xyz:

average rate = 3d/(yzd/xyz + xzd/xyx + xyd/xyz)

average rate = 3d/[(yzd + xzd + xyd)/xyz]

average rate = 3d * xyz/(yzd + xzd + xyd)

average rate = 3d * xyz/[d(yz + xz + xy)]

The ds cancel and we are left with:

3xyz/(yz + xz + xy)

_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Non-Human User Joined: 09 Sep 2013
Posts: 15592
Re: Jacob drove from Town A to Town B at an average rate of x miles per ho  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Jacob drove from Town A to Town B at an average rate of x miles per ho   [#permalink] 30 May 2020, 21:56

# Jacob drove from Town A to Town B at an average rate of x miles per ho  