GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Dec 2018, 03:57

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# Frederique traveled x/8 of the total distance of a trip

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Nov 2013
Posts: 89
Frederique traveled x/8 of the total distance of a trip  [#permalink]

### Show Tags

29 Sep 2016, 17:37
5
00:00

Difficulty:

35% (medium)

Question Stats:

76% (03:25) correct 24% (02:34) wrong based on 117 sessions

### HideShow timer Statistics

this question comes from Prep4Gmat app

Frederique traveled x/8 of the total distance of a trip at an average speed of 40 miles per hour, where 1=<x=<7. She traveled the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Frederique's average speed for the entire trip?

A) (180-x)/2
B) (x+60)/4
C) (300-x)/8
D) 800/(120+x)
E) 960/(x+16)
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4488
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

### Show Tags

30 Sep 2016, 10:19
4
lalania1 wrote:
this question comes from Prep4Gmat app

Frederique traveled x/8 of the total distance of a trip at an average speed of 40 miles per hour, where 1=<x=<7. She traveled the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Frederique's average speed for the entire trip?

A) (180-x)/2
B) (x+60)/4
C) (300-x)/8
D) 800/(120+x)
E) 960/(x+16)

Dear lalania1,

I'm happy to respond.

Here's a blog you might find germane:
GMAT Distance and Work: Rate Formula

Here's my solution.

There are two legs in the trip. Call the total distance D. In the first leg, she covers a distance of D*(x/8) at a speed of 40 mph, and in the second leg, she covers a distance of D*((8 - x)/8) at a speed of 60 mph.

We need to calculate the time in each leg. Since D = RT, we know that T = D/R.

$$T_1 = \frac{x}{8}*D \div 40 = \frac{xD}{8*40}$$

$$T_2 = \frac{(8-x)}{8}*D \div 60 = \frac{(8-x)D}{8*60}$$

Leave the denominators unmultiplied for the moment.

$$T_{total} = T_1 + T_2 = \frac{xD}{8*40} + \frac{(8-x)D}{8*60}$$

$$T_{total} = \frac{3xD}{8*120} + \frac{2(8-x)D}{8*120}$$

$$T_{total} = \frac{(16 + x)D}{8*120} = \frac{(16 + x)D}{960}$$

Now, to find the average velocity, divide the total distance D by the total time.

$$v_{average} = \frac{D}{T_{total}} = D \times \frac{960}{(16 + x)D} = \frac{960}{(16 + x)}$$

Does all this make sense?

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Current Student
Joined: 06 Jul 2016
Posts: 39
Location: India
Concentration: Operations, General Management
GMAT 1: 610 Q49 V25
WE: General Management (Energy and Utilities)
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

### Show Tags

30 Sep 2016, 11:44
1
Hi,

I used 'plugging in' approach to solve this.

Let total distance is 200 miles and X=4.

So, half(4/8) of the distance i.e. 100 miles was traveled at 40 mph and rest 100 at 60 mph.

Thus, the average speed will be (2*40*60)/(40+60)=48.

Now plugging in the value of x in the answer choices, we get E as 48.

Regards,

Amulya
Manager
Joined: 17 Nov 2013
Posts: 89
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

### Show Tags

01 Oct 2016, 09:57
I think for me it is easier to use smart numbers

Step1: smart numbers d=200 and x=4. Why? well they are easy to use. I could have used d=240 too to keep it easier but I wanted to use the same numbers that a prior user did so to compare and contrast.
step2: identify what the question is asking. the question is asking the Rt, so that is Rt= Dt/Tt. it also asks to provide the answer in terms of x, so that means that at the very end I will have to use x=4 to plug and find the Rt that I get in my execution part.
step3: solve for R(t)

R T = D
40 t1 = (4/8) 200 => t1 = 5/2
60 t2 = (4/8) 200 => t2 = 5/3

R(t) T(t) = D(t)
R(t) = D(t)/T(t) = 200/(5/2 + 5/3) = 48

Step4: refresh your memory, so you are using x=4 replace it into the answers to find out which one gives 48. => 960/(4+16) => 960/20 = 48. Answer E is the correct answer.
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 518
Location: India
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

### Show Tags

27 Feb 2017, 02:58
if x =8, average speed will come 40 and if x =0 average speed will come 60. Checking the options we get option E as answer.
_________________

GMAT Mentors

Non-Human User
Joined: 09 Sep 2013
Posts: 9199
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

### Show Tags

06 Aug 2018, 01:51
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: Frederique traveled x/8 of the total distance of a trip &nbs [#permalink] 06 Aug 2018, 01:51
Display posts from previous: Sort by