A car traveling uphill will take an hour less to cover the : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 13:02

### 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 June
Open Detailed Calendar

# A car traveling uphill will take an hour less to cover the

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 15 Jun 2010
Posts: 368
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 11

Kudos [?]: 369 [0], given: 50

A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

08 Aug 2012, 05:40
13
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

71% (04:24) correct 29% (03:06) wrong based on 127 sessions

### HideShow timer Statistics

A car traveling uphill will take an hour less to cover the distance if it moved 4km/hr faster. On the other hand it will take 3 more hours to reach the destination if it moved 6km/hr slower. What is the distance that the car travels?

A. 50
B. 80
C. 105
D. 75
E. 65

Source: 4gmat
[Reveal] Spoiler: OA

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93350 [2] , given: 10557

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

08 Aug 2012, 06:14
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
SOURH7WK wrote:
A car traveling uphill will take an hour less to cover the distance if it moved 4km/hr faster. On the other hand it will take 3 more hours to reach the destination if it moved 6km/hr slower. What is the distance that the car travels?

A. 50
B. 80
C. 105
D. 75
E. 65

Source: 4gmat

ALGEBRAIC WAY:

Say it takes the car $$t$$ hours to cover the distance at $$r$$ kilometers per hour, so $$d=tr$$. We are told that:

$$tr=(t-1)(r+4)$$ --> $$tr=tr+4t-r-4$$ --> $$4t-r-4=0$$;
$$tr=(t+3)(r-6)$$ --> $$tr=tr-6t+3r-18$$ --> $$r-2t-6=0$$;

Solving gives: $$t=5$$ and $$r=16$$ --> $$d=tr=80$$.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93350 [1] , given: 10557

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

17 Aug 2012, 04:46
1
KUDOS
Expert's post
rajathpanta wrote:
Hi bunuel, Is there a simpler way to solve this problem. I am stuck. There are 3 unknowns and only 2 equations can be formed. Unable to comprehend the above method.

We have:
$$tr=(t-1)(r+4)$$ --> $$tr=tr+4t-r-4$$ --> $$4t-r-4=0$$;
$$tr=(t+3)(r-6)$$ --> $$tr=tr-6t+3r-18$$ --> $$r-2t-6=0$$;

So, we get two distinct linear equations with two unknowns ($$4t-r-4=0$$ and $$r-2t-6=0$$) --> we can solve for $$t$$ and $$r$$. Now, since $$distance=tr$$, then we can get the distance too.

Hope it's clear.
_________________
Director
Status: Enjoying the GMAT journey....
Joined: 26 Aug 2011
Posts: 735
Location: India
GMAT 1: 620 Q49 V24
Followers: 72

Kudos [?]: 504 [1] , given: 264

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

17 Aug 2012, 21:09
1
KUDOS
1
This post was
BOOKMARKED
arichardson26 wrote:
Hi could you explain why you set the two rate/time combinations equal to 0?

tr=(t-1)(r+4) --> tr=tr+4t-r-4 --> 4t-r-4=0;
tr=(t+3)(r-6) --> tr=tr-6t+3r-18 --> r-2t-6=0

tr=(t-1)(r+4) --> tr=tr+4t-r-4--> Take the tr on the left hand side to the right hand side, the sigh of the moving tr changes and it gets cancelled,whereas the left hand side is left with nothing but zero....Same way for the second part also..
_________________

Fire the final bullet only when you are constantly hitting the Bull's eye, till then KEEP PRACTICING.

A WAY TO INCREASE FROM QUANT 35-40 TO 47 : http://gmatclub.com/forum/a-way-to-increase-from-q35-40-to-q-138750.html

Q 47/48 To Q 50 + http://gmatclub.com/forum/the-final-climb-quest-for-q-50-from-q47-129441.html#p1064367

Three good RC strategies http://gmatclub.com/forum/three-different-strategies-for-attacking-rc-127287.html

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 274
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 89 [0], given: 282

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

13 Aug 2012, 03:03
Hi bunuel, Is there a simpler way to solve this problem. I am stuck. There are 3 unknowns and only 2 equations can be formed. Unable to comprehend the above method.
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Intern
Joined: 28 May 2012
Posts: 2
Followers: 0

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

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

17 Aug 2012, 21:01
Hi could you explain why you set the two rate/time combinations equal to 0?

tr=(t-1)(r+4) --> tr=tr+4t-r-4 --> 4t-r-4=0;
tr=(t+3)(r-6) --> tr=tr-6t+3r-18 --> r-2t-6=0
Senior Manager
Joined: 15 Jun 2010
Posts: 368
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 11

Kudos [?]: 369 [0], given: 50

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

19 Aug 2012, 02:48
1
This post was
BOOKMARKED
arichardson26 wrote:
Hi could you explain why you set the two rate/time combinations equal to 0?

tr=(t-1)(r+4) --> tr=tr+4t-r-4 --> 4t-r-4=0;
tr=(t+3)(r-6) --> tr=tr-6t+3r-18 --> r-2t-6=0

To get 2 simultaneous equation to solve 2 unknown variables.

4t-r=4 Eq 1
r-2t=6 Eq 2
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Intern
Joined: 11 Jul 2012
Posts: 46
Followers: 0

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

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

17 Sep 2012, 05:55
My approach
d/r - d/(r+4) = 1 ( i) (time lag)
d/(r-6) + d/r = 3 (ii) (time lag)
From (i) d = r(r+4)/4 (iii)
From (ii) d = r(r-6)/2 (iv)
(iii) = (iv) => r = 16
and r = 16 in (iii) => d = 80
Brother Karamazov
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13486
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

10 Nov 2014, 05:26
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.
_________________
Manager
Joined: 27 May 2014
Posts: 85
Followers: 0

Kudos [?]: 19 [0], given: 21

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

10 Nov 2014, 20:22
Bunuel - in cases such as this when time and rate are unknown but distance is the same, are these always solvable? I'm thinking more along the lines of data sufficiency
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13486
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: A car traveling uphill will take an hour less to cover the [#permalink]

### Show Tags

30 May 2016, 21:47
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 car traveling uphill will take an hour less to cover the   [#permalink] 30 May 2016, 21:47
Similar topics Replies Last post
Similar
Topics:
The time it took car P to travel 600 miles was 2 hours less than the 1 31 Jul 2016, 03:17
1 In the first hour of a two-hour trip, a car traveled d kilometers, and 4 12 Nov 2015, 01:05
10 A car travelling from city A to B takes an hour lesser to cover the 9 30 Aug 2014, 02:37
A bicyclist travels uphill from town A to town B for 2 hours at an ave 4 28 Jun 2011, 22:15
14 The time it took car A to travel 400 miles was 2 hours less 9 10 Mar 2011, 09:42
Display posts from previous: Sort by