It is currently 17 Oct 2017, 12:19

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A driver completed the first 20 miles of a 40-mile trip at a

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [0], given: 12180

A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Mar 2014, 15:05
Expert's post
20
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:51) correct 25% (03:05) wrong based on 757 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)

(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph

Problem Solving
Question: 142
Category: Algebra Applied problems
Page: 80
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128579 [0], given: 12180

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [2], given: 12180

Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Mar 2014, 15:05
2
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
SOLUTION

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)

(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph

\(average \ speed=\frac{total \ distance}{total \ time}=\frac{40}{total \ time}=60\). This implies that for the average time to be 60 miles per hour, the total time must be 40/60 = 2/3 hours.

Now, the first 20 miles were covered in (time) = (distance)/(speed) = 20/50 = 2/5 hours.

Thus, the remaining 20 miles should be covered in 2/3 - 2/5 = 4/15 hours, which means that the remaining 20 miles should be covered at an average speed (distance)/(time) = 20/(4/15) = 75 miles per hour.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128579 [2], given: 12180

2 KUDOS received
Intern
Intern
User avatar
Affiliations: CA, SAP FICO
Joined: 22 Nov 2012
Posts: 33

Kudos [?]: 12 [2], given: 51

Location: India
Concentration: Finance, Sustainability
Schools: Mannheim"18
GMAT 1: 620 Q42 V33
GMAT 2: 720 Q47 V41
GPA: 3.2
WE: Corporate Finance (Energy and Utilities)
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Mar 2014, 18:40
2
This post received
KUDOS
Speed = Distance/ Time

Time elapsed for 20Miles = (20/50) *60 = 24 Min
Remaining distance = 20 Miles

Remaining time:
@ 60 Miles/ hr, 40 Miles would take - 40 Minutes

So remaining time = 40-24 = 16 Mins

Speed required to cover 20 miles in 16 mins = (20/16)*60 = 75 Miles/hr

Kudos [?]: 12 [2], given: 51

11 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2616 [11], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Mar 2014, 19:32
11
This post received
KUDOS
1
This post was
BOOKMARKED
Answer = (D) 75 mph

Time = Distance / Speed

Setting up equation as shown in fig
Attachments

dis.jpg
dis.jpg [ 26.29 KiB | Viewed 7415 times ]


_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2616 [11], given: 193

3 KUDOS received
Current Student
User avatar
Joined: 25 Sep 2012
Posts: 288

Kudos [?]: 173 [3], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
GMAT ToolKit User Reviews Badge
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Mar 2014, 22:15
3
This post received
KUDOS
1
This post was
BOOKMARKED
Average speed concept always confuses me. Anyways there is a formula

\(Avg. Speed = \frac{2(S_1)(S_2)}{S_1+S_2}\)


\(S_1\) being one speed and \(S_2\) being another

By substituting the value you will get 75 miles/hour


Answer D
Time Taken - 1:45
Difficulty level - 600

Kudos [?]: 173 [3], given: 242

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 267

Kudos [?]: 106 [1], given: 29

Location: India
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Mar 2014, 23:49
1
This post received
KUDOS
Option D.
First 20 miles covered at 50 miles/hr.
Time taken=D/S=2/5 hrs.
Total time=Total D/Avg speed for entire journey.=40/60=2/3 hrs.
Time left=2/3-2/5=4/15 hrs.
Distance left=20 miles
Therefore speed should be D/T=20/(4/15)=75mph

Kudos [?]: 106 [1], given: 29

Intern
Intern
avatar
Joined: 30 Jan 2014
Posts: 15

Kudos [?]: 1 [0], given: 15

GMAT ToolKit User
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 11 Mar 2014, 08:12
b2bt wrote:
Average speed concept always confuses me. Anyways there is a formula

\(Avg. Speed = \frac{2(S_1)(S_2)}{S_1+S_2}\)


\(S_1\) being one speed and \(S_2\) being another

By substituting the value you will get 75 miles/hour


Answer D
Time Taken - 1:45
Difficulty level - 600



What are (S1) and (S2) ?

Kudos [?]: 1 [0], given: 15

Current Student
User avatar
Joined: 25 Sep 2012
Posts: 288

Kudos [?]: 173 [0], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
GMAT ToolKit User Reviews Badge
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 11 Mar 2014, 10:15
lool wrote:
b2bt wrote:
Average speed concept always confuses me. Anyways there is a formula

\(Avg. Speed = \frac{2(S_1)(S_2)}{S_1+S_2}\)


\(S_1\) being one speed and \(S_2\) being another

By substituting the value you will get 75 miles/hour


Answer D
Time Taken - 1:45
Difficulty level - 600



What are (S1) and (S2) ?



Here \(S_1\) = 50 and \(S_2\) = \(x\) Average Speed = 60. Insert these value in formula and you will find x :)
BTW, for this formula to work, the distance covered should be the same. In this case distance = 20 in each case. If you are interested, I can explain you how this formula is derived. Just reply back :)

Kudos [?]: 173 [0], given: 242

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 593

Kudos [?]: 458 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 18 Aug 2015, 03:22
Total Distance =40 km
Total Time = 20/50 + 20/X (X=average speed for the remaining 20km)
Required Average Speed = 60
Formula => Average speed = Total Distance / Total Time --> 40/(20/50 + 20/X)=60; X=75 (D)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 458 [0], given: 200

Manager
Manager
User avatar
Joined: 05 Jul 2015
Posts: 107

Kudos [?]: 27 [0], given: 3

Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3
A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 22 Nov 2015, 16:49
My way was the same as everyone else's until the end. Still got the right answer though.

(Total Distance 40 / Total time ) = 60
So 40/60th of an hour means 40 minutes.

20/50 = 24 minutes

40-24=16

24:16 is 3:2 so 2x=50 so 3x=75

Kudos [?]: 27 [0], given: 3

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 810

Kudos [?]: 247 [0], given: 12

Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 07 Feb 2017, 13:48
A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)

(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph

r=speed needed to average 60 mph for trip
total distance=40 miles
total time=2/5+20/r
40/(2/5+20r)=60
r=75 mph
D

Kudos [?]: 247 [0], given: 12

Senior Manager
Senior Manager
User avatar
S
Joined: 24 Oct 2016
Posts: 319

Kudos [?]: 25 [0], given: 88

Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 11 Feb 2017, 02:00
the above problem can be solved with in 50sec. by plugging the answer choices in the avg speed formula as the distance is constant then we use this formula 2xy/x+y where x and y are the avg. speeds. so the only value which satisfies the avg speed equal to 60km/hr. is 75, ex. 2*75*50/125= 60
hence the answer is D
thanks
if you liked my post please kudos :)

Kudos [?]: 25 [0], given: 88

Manager
Manager
User avatar
B
Joined: 21 Jul 2017
Posts: 80

Kudos [?]: 8 [0], given: 59

Location: India
Concentration: Social Entrepreneurship, Leadership
GMAT 1: 750 Q51 V41
GPA: 4
CAT Tests
Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 17 Sep 2017, 05:31
b2bt wrote:
Average speed concept always confuses me. Anyways there is a formula

\(Avg. Speed = \frac{2(S_1)(S_2)}{S_1+S_2}\)


\(S_1\) being one speed and \(S_2\) being another

By substituting the value you will get 75 miles/hour


Answer D
Time Taken - 1:45
Difficulty level - 600


Everyone please not you can only use this approach when the distance is same i.e., If the distance covered is constant then the average speed is Harmonic mean of the values. Else the traditional formula approach must be used.

Kudos [?]: 8 [0], given: 59

Manager
Manager
User avatar
B
Joined: 21 Jun 2017
Posts: 70

Kudos [?]: 4 [0], given: 2

Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 09 Oct 2017, 09:57
A table helps solve this problem. This problem involves the fundamental principle of Time x Rate = Distance. Therefore, Time = Distance/Rate.
First trip, T = 2/5; Total Trip, T = 2/3
2/5 + 20/s = 2/3
isolate the variable: 20/s = 2/3 - 2/5
20/s = 10/15 - 6/15
20/s = 4/15; looking at the ratio, for every 4 there is 20; thus, 5
5 x 15 = s = 75
Thus, the answer is (D) 75 mph


hope this helps

Kudos [?]: 4 [0], given: 2

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 827 [0], given: 5

Re: A driver completed the first 20 miles of a 40-mile trip at a [#permalink]

Show Tags

New post 12 Oct 2017, 18:02
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)

(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph


We can use the following formula:

average rate = (distance 1 + distance 2)/(time 1 + time 2)

where average rate = 60, distance 1 = distance 2 = 20, time 1 = distance 1/rate 1 = 20/50 = 2/5, and time 2 = distance 2/rate 2 = 20/r (where r is the average speed of the remaining 20 miles).

Let’s now determine r:

60 = (20 + 20)/(2/5 + 20/r)

60 = 40/(2r/5r + 100/5r)

60 = 40/[(2r + 100)/5r]

60 = 200r/(2r + 100)

60(2r + 100) = 200r

120r + 6000 = 200r

6000 = 80r

r = 6000/80 = 600/8 = 75

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

Kudos [?]: 827 [0], given: 5

Re: A driver completed the first 20 miles of a 40-mile trip at a   [#permalink] 12 Oct 2017, 18:02
Display posts from previous: Sort by

A driver completed the first 20 miles of a 40-mile trip at a

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.