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

 It is currently 22 Oct 2019, 19:55 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.  Frederique traveled x/8 of the total distance of a trip

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 17 Nov 2013
Posts: 77
Frederique traveled x/8 of the total distance of a trip  [#permalink]

Show Tags

7 00:00

Difficulty:   45% (medium)

Question Stats: 73% (03:20) correct 27% (02:49) wrong based on 127 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 G
Joined: 28 Dec 2011
Posts: 4472
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

Show Tags

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 B
Joined: 06 Jul 2016
Posts: 38
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

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: 77
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

Show Tags

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  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

Show Tags

1
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 Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8134
Location: United States (CA)
Re: Frederique traveled x/8 of the total distance of a trip  [#permalink]

Show Tags

1
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)

We can let 80 be the total distance and use the formula of average rate = total distance/total time; thus, we have:

average = 80/[(x/8 * 80)/40 + ((8 - x)/8 * 80)/60]

average = 80/[10x/40 + 10(8 - x)/60]

average = 80/[x/4 + (8 - x)/6]

Multiplying by 12/12, we have:

average = 960/[3x + 2(8 - x)]

average = 960/[(x + 16)

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Frederique traveled x/8 of the total distance of a trip   [#permalink] 16 Sep 2019, 11:33
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  