It is currently 18 Nov 2017, 15:02

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A cyclist bikes x distance at 10 miles per hour and returns

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Oct 2009
Posts: 8

Kudos [?]: 11 [1], given: 1

A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

12 Oct 2009, 13:02
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

74% (01:14) correct 26% (00:57) wrong based on 292 sessions

### HideShow timer Statistics

A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0
[Reveal] Spoiler: OA

Kudos [?]: 11 [1], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132612 [3], given: 12326

Re: Average rate on round trip [#permalink]

### Show Tags

12 Oct 2009, 13:16
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
timmaxwell8 wrote:
18. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0

Let the distance be 40 miles (40 because it's divisible by 10 and 8)

Time for 1st trip=40/10=4 hours
Time back =40/8=5hours

Average rate=total distance/total time=(40+40)/(4+5)=80/9=8.9

D.

It's possible to write the formula with variable x for distance but the above way is fastest.

Here is the formula if you need it:
Av rate=(x+x)/(x/10+x/8)=80/9=8.9
_________________

Kudos [?]: 132612 [3], given: 12326

Intern
Joined: 04 Oct 2009
Posts: 19

Kudos [?]: 10 [1], given: 2

GMAT 1: 730 Q49 V40
GPA: 3.22
Re: Average rate on round trip [#permalink]

### Show Tags

12 Oct 2009, 22:12
1
KUDOS
total distance = 2x
Time on the way there is (x miles)/(10 miles/hour)= x/10 hours
Time on the way back is (x miles)/(8 miles/hour)= x/8 hours
Total time=(x/10)+(x/8)=(9x/40) hours

Average rate=(total distance)/(total time)
x is a dummy variable and will cancel out
Average rate=(2x)miles/(9x/40)hour= 80/9 mph=8.9 mph D

Kudos [?]: 10 [1], given: 2

Manager
Affiliations: CFA Level 2 Candidate
Joined: 29 Jun 2009
Posts: 218

Kudos [?]: 291 [0], given: 2

Schools: RD 2: Darden Class of 2012
Re: Average rate on round trip [#permalink]

### Show Tags

13 Oct 2009, 14:24
Pick numbers that make sense. 8x10--> 80 miles

1st Trip takes 8 hours at 10/mph
2nd Trip takes 10 hours at 8/mph

160/18
= 8.9mph

Kudos [?]: 291 [0], given: 2

Intern
Joined: 18 Nov 2009
Posts: 3

Kudos [?]: [0], given: 0

Schools: CMU, MIT, ASU, BYU, MSU
Re: Average rate on round trip [#permalink]

### Show Tags

02 Jan 2010, 14:15
Another approach to roundtrip average rates is to conceptually utilize weighting. Because time is a weight here, slightly more time, or weight, is used at 8 mph than 10 mph, so the average rate should be slightly closer to 8 mph than it is to 10 mph. Answer 8.9 mph.

Phew...I finally made my first post.
_________________

"You can go far if you only try."

Kudos [?]: [0], given: 0

Manager
Joined: 18 Jan 2011
Posts: 228

Kudos [?]: 37 [0], given: 4

Re: Average rate on round trip [#permalink]

### Show Tags

17 Apr 2011, 13:17
the avg speed formula does the trick ...
_________________

Good Luck!!!

***Help and be helped!!!****

Kudos [?]: 37 [0], given: 4

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1602

Kudos [?]: 600 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Re: Average rate on round trip [#permalink]

### Show Tags

17 Apr 2011, 21:54
2x/(x/10 + x/8)

= 2/(1/10 + 1/8)

= 2 * 40/(4 + 5)

= 80/9 = 8.88 ~ 8.9

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 600 [0], given: 40

Manager
Joined: 10 Jul 2010
Posts: 193

Kudos [?]: 20 [0], given: 12

Re: Average rate on round trip [#permalink]

### Show Tags

18 Apr 2011, 00:01
Substitute a number in for X

RT=D

R T D
--------------------------------
a 10 40
b 8 40

I chose the common multiple 40, so now since average rate = total distance/total time we need to find time

rt=d --? t=d/4

so

R T D
--------------------------------
a 10 4 40
b 8 5 40
---------------------------------------
total 9 80

r=80/9

r=8.888888 --> ~8.9 so D is the answer

Kudos [?]: 20 [0], given: 12

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 281 [0], given: 0

Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

07 Jan 2014, 11:20
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.
_________________

Kudos [?]: 281 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 281 [0], given: 0

Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

05 Nov 2016, 15:59
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.
_________________

Kudos [?]: 281 [0], given: 0

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3097

Kudos [?]: 1114 [0], given: 327

Location: India
GPA: 3.5
Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

06 Nov 2016, 03:24
timmaxwell8 wrote:
A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0

Let x = 40 ( LCM of 10 & 8 )

So, Time taken for onward journey = 4 hrs
And, Time taken for return journey = 5 hrs

So, total time taken = 9 hrs

Hence, average speed = 2*40/9 => 8.89 Hrs

Thus, answer will be (D) 8.9 hours..

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1114 [0], given: 327

Intern
Joined: 06 May 2015
Posts: 25

Kudos [?]: 2 [0], given: 99

Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

10 Jul 2017, 02:19
the best way to solve avg speed when same distance is convered by two dift velocity

Avg speed = 2ab/a+b

so 2x10x8/18 =8.9 so answer is D

Kudos [?]: 2 [0], given: 99

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1806

Kudos [?]: 920 [0], given: 3

Location: United States (CA)
Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

12 Jul 2017, 17:02
timmaxwell8 wrote:
A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0

We can use the formula average speed = total distance/total time. Since the distance for each leg traveled is x, the total distance is 2x, the time going is x/10, and the time coming back is x/8. We have:

average = 2x/(x/10 + x/8)

average = 2x/(4x/40 + 5x/40)

average = 2x/(9x/40)

average = (2x)(40/9x)

average = 80/9 = 8.9

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 920 [0], given: 3

Director
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: A cyclist bikes x distance at 10 miles per hour and returns [#permalink]

### Show Tags

13 Aug 2017, 12:56
timmaxwell8 wrote:
A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0

This is clearly a round trip question so we should consider the formula

Total Distance= AvgSpeed * Time Spent

And also that

Distance1= Distance2 (we hold the distance constant because of course the distance on each trip is obviously the same)

Now we can just plug in a simple value

40/8 = 5 hours

40/10= 4 hours

80miles= Avgspeed * 9 hours

80/9= 8.888888 so round up

D

Kudos [?]: 36 [0], given: 165

Re: A cyclist bikes x distance at 10 miles per hour and returns   [#permalink] 13 Aug 2017, 12:56
Display posts from previous: Sort by