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

 It is currently 19 Jul 2018, 12:33

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47112
A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

09 Mar 2014, 15:05
3
25
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:56) correct 24% (02:37) wrong based on 1106 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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

09 Mar 2014, 15:05
5
10
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.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
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

09 Mar 2014, 19:32
13
4

Time = Distance / Speed

Setting up equation as shown in fig
Attachments

dis.jpg [ 26.29 KiB | Viewed 9953 times ]

_________________

Kindly press "+1 Kudos" to appreciate

##### General Discussion
Intern
Affiliations: CA, SAP FICO
Joined: 22 Nov 2012
Posts: 35
Location: India
Concentration: Finance, Sustainability
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

09 Mar 2014, 18:40
2
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
Current Student
Joined: 25 Sep 2012
Posts: 271
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

09 Mar 2014, 22:15
3
1
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

Time Taken - 1:45
Difficulty level - 600
Manager
Joined: 20 Dec 2013
Posts: 249
Location: India
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

09 Mar 2014, 23:49
1
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
Intern
Joined: 30 Jan 2014
Posts: 13
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

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

Time Taken - 1:45
Difficulty level - 600

What are (S1) and (S2) ?
Current Student
Joined: 25 Sep 2012
Posts: 271
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

11 Mar 2014, 10:15
1
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

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
Director
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

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.

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

Manager
Joined: 05 Jul 2015
Posts: 104
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

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
VP
Joined: 07 Dec 2014
Posts: 1036
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

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
Senior Manager
Joined: 24 Oct 2016
Posts: 294
Location: India
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

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
thanks
if you liked my post please kudos
Manager
Joined: 21 Jul 2017
Posts: 139
Location: India
GMAT 1: 650 Q47 V33
GPA: 4
WE: Project Management (Education)
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

17 Sep 2017, 05:31
1
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

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.
Manager
Joined: 21 Jun 2017
Posts: 78
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

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
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

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

_________________

Jeffery Miller

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

CEO
Joined: 12 Sep 2015
Posts: 2633
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

10 Dec 2017, 10:52
1
Top Contributor
1
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

The total distance is 40 miles, and we want the average speed to be 60 miles per hour.
Average speed = (total distance)/(total time)
So, we get: 60 = (40 miles)/(total time)
Solve equation to get: total time = 2/3 hours
So, the TIME for the ENTIRE 40-mile trip needs to be 2/3 hours.

driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour.
How much time was spent on this FIRST PART of the trip?
time = distance/speed
So, time = 20/50 = 2/5 hours

The ENTIRE trip needs to be 2/3 hours, and the FIRST PART of the trip took 2/5 hours

2/3 hours - 2/5 hours = 10/15 hours - 6/15 hours
= 4/15 hours
So, the SECOND PART of the trip needs to take 4/15 hours

The SECOND PART of the trip is 20 miles, and the time is 4/15 hours
Speed = distance/time
So, speed = 20/(4/15)
= (20)(15/4)
= 75

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 17 Jul 2016
Posts: 35
A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

15 Dec 2017, 09:47
$$rate * time = distance$$

$$50 * \frac{2}{5} = 20$$

$$x * \frac{20}{x} =20$$

$$total distance=20 +20$$

$$total time = 2/5+20/x$$

$$\frac{(20+20)}{(2/5+20/x)}=60$$

solving for x gives 75
Intern
Joined: 11 Dec 2016
Posts: 33
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

12 Apr 2018, 11:33
VeritasPrepKarishma
Hi. I'm sorry for bothering you again. I just wanted to know how the scale method can be used for this specific problem? I'd be grateful.
Intern
Joined: 11 Dec 2016
Posts: 33
A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

12 Apr 2018, 11:41
1
VeritasPrepKarishma

I figured out. Sorry!

It's like:

t1/t2=(x-60)/(60-50)

Where t1= 2/5 & t2= 20/x

The equation looks something like this after solving a bit
2x/5*20=(x-60)/10
x=5(x-60)
X=5x-300
4x=300
x= 75

Option D
GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: A driver completed the first 20 miles of a 40-mile trip at a  [#permalink]

### Show Tags

12 Apr 2018, 21:18
1
1
asfandabid wrote:
VeritasPrepKarishma

I figured out. Sorry!

It's like:

t1/t2=(x-60)/(60-50)

Where t1= 2/5 & t2= 20/x

The equation looks something like this after solving a bit
2x/5*20=(x-60)/10
x=5(x-60)
X=5x-300
4x=300
x= 75

Option D

Though you have applied the scale method correctly, I would like to point out that the best method to use here is the formula 2ab/(a+b)
When one drives at speed a for half the distance and at speed b for the other half of the distance, the average speed is given by 2ab/(a+b)

60 = 2*50*b/(50 + b)
b = 3000/40 = 75

Check this post for these formulas: https://www.veritasprep.com/blog/2015/0 ... -the-gmat/
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Re: A driver completed the first 20 miles of a 40-mile trip at a &nbs [#permalink] 12 Apr 2018, 21:18
Display posts from previous: Sort by

# Events & Promotions

 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®.