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

 It is currently 12 Dec 2019, 11:24

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 hiker walked for two days. On the second day the hiker wal

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

Hide Tags

Manager
Joined: 28 Aug 2010
Posts: 149
A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

24 Dec 2010, 07:58
3
1
13
00:00

Difficulty:

25% (medium)

Question Stats:

78% (02:32) correct 22% (02:49) wrong based on 416 sessions

HideShow timer Statistics

A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?

(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: A hiker walked for two days  [#permalink]

Show Tags

24 Dec 2010, 08:22
9
1
12
ajit257 wrote:
A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles
and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph

ALGEBRAIC APPROACH:

As on the second day the hiker walked 2 hours longer than he walked on the first day and spent a total of 18 hours walking then t+(t+2)=18 --> t=8. So the hiker walked 8 hours on the first day and 10 hours on the second day;

Let the rate on the first day be r then: 8r+10(r+1)=64 --> r=3.

10 SECOND APPROACH:

Average rate of the hiker is (total distance)/(total time)=64/18=~3.6, now r<3.6<r+1 (the weighted average of 2 individual averages, r and r+1, must lie between these individual averages) --> only answer choice B fits.

_________________
General Discussion
Manager
Joined: 07 Jan 2010
Posts: 103
Location: So. CA
WE 1: 2 IT
WE 2: 4 Software Analyst
Re: A hiker walked for two days  [#permalink]

Show Tags

25 Dec 2010, 13:39
ron covered this problem in his workshop on Rate/Time/Distance (April 29, 2010)
http://www.manhattangmat.com/thursdays-with-ron.cfm
Manager
Joined: 27 Jul 2010
Posts: 132
Location: Prague
Schools: University of Economics Prague
Re: A hiker walked for two days  [#permalink]

Show Tags

25 Dec 2010, 16:32
10 sec approach is great
Senior Manager
Joined: 08 Nov 2010
Posts: 268
WE 1: Business Development
Re: A hiker walked for two days  [#permalink]

Show Tags

25 Dec 2010, 18:34
yep, liked the 10 sec app as well...
Manager
Status: I am Midnight's Child !
Joined: 04 Dec 2009
Posts: 80
WE 1: Software Design and Development
Re: A hiker walked for two days  [#permalink]

Show Tags

22 Feb 2011, 15:03
Let x be the number of miles in first day ; 64-x = number of miles in second day
given,
t+ t+2 =18 -> t=10
Speed in first day = speed in second day - 1

Therefore, $$(64-x)/10$$ - $$x/8$$ = 1

x = 24

Therefore, speed = $$d/t$$ = $$24/8$$ = $$3$$
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

27 Jun 2013, 02:25
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Distance/Rate Problems: distance-speed-time-word-problems-made-easy-87481.html

All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
All PS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=64

_________________
Director
Joined: 17 Dec 2012
Posts: 623
Location: India
Re: A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

27 Jun 2013, 19:02
5
3
1. Average speed for the first 2 days is 64/18 = 3.6 approx. Since the speed on the first day is lower than that on the second day, the speed on the first day should be less than 3.6 . Only A and B fit this requirement
2. It cannot be choice A because if the speed on the first day is 2 miles/hr then the speed on the second day would be 3 miles/hr and so the average speed cannot be 3.6 miles/hr.

So the answer is choice B.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Senior Manager
Joined: 13 May 2013
Posts: 396
Re: A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

05 Aug 2013, 14:24
1
A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?

Hiker walked for two days for a total of 18 hours. He spent two more hours walking on the second day than the first: h1+h2=18 ===> h+h+2 = 18 ===> 2h = 16 ===> h=8.
He spent 8 hours the first day and 10 hours the second day.
Day 1 = 8h
Day 2 = 10h

Average speed = total distance/combined rate
Average speed = 64/r1+r2

rate = distance/time
r = d/8
r+1 = d/10 ===> r = (d/10)-1

64/(d/8) + (d/10)-1

Why wouldn't I use that formula? Is it because I would be trying to figure out average speed when I don't know the speed of the hiker on day one or two?

distance=rate*time
d1=r*8
d2=(r+1)*10

d1+d2=total distance
d1+d2=64
(r8)+(10r+10)=64
18r=64
r=3

ANSWER: (B) 3 mph
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8255
GMAT 1: 760 Q51 V42
GPA: 3.82
A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

30 Aug 2015, 14:16
1
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

1-st day: vt=d1(v:velocity, t:time taken, d1:distance)
2-nd day: (v+1)(t+2)=d2 and d1+d2=64

t+t+2=18, 2t=16, t=8 and 8v=d1 <-- equation 1), 10(v+1)=d2, 10v+10=d2 <-- equation 2)

equation 1)+ equation 2), then 8v+10v+10=d1+d2=64, 18v=54, v=3

Therefore the answer is B. thank you!!
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15704
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

14 Feb 2018, 16:27
1
Hi All,

This question requires a certain degree of note-taking and organization. Once you've got everything on the pad, you can then approach the math in a couple of ways:

Since we're dealing with distance, rate and time, I'm going to make two equations based on the two days of travel:

Day 1: Distance = (R mph)(T hours)
Day 2: Distance#2 = (R+1 mph)(T+2 hours)

Since the TOTAL TIME for both days was 18 hours, we can solve for T...

T + (T+2) = 18
2T = 16
T = 8

Since the TOTAL DISTANCE for both days was 64 miles, we can now set up 1 gigantic equation....

64 miles = (R)(8) + (R+1)(10)

At this point, we have 1 variable and 1 equation, so we can solve for R....

64 = 8R + 10R + 10
54 = 18R
3 = R

The prompt asks for the speed on DAY 1; since the hiker traveled R mph on Day 1, the answer is 3...

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
Joined: 09 Sep 2013
Posts: 13744
Re: A hiker walked for two days. On the second day the hiker wal  [#permalink]

Show Tags

06 Apr 2019, 02:33
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: A hiker walked for two days. On the second day the hiker wal   [#permalink] 06 Apr 2019, 02:33
Display posts from previous: Sort by

A hiker walked for two days. On the second day the hiker wal

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

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