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

 It is currently 15 Oct 2019, 14:22

### 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 man covers a certain distance in a train. If the train mov

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Nov 2013
Posts: 24
Location: India
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

Updated on: 05 Feb 2014, 23:55
1
10
00:00

Difficulty:

55% (hard)

Question Stats:

70% (03:17) correct 30% (03:06) wrong based on 98 sessions

### HideShow timer Statistics

A man covers a certain distance in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?

A. 200 km
B. 50 km
C. 20 km
D. 60 km
E. 80 km

Originally posted by manish2014 on 05 Feb 2014, 22:59.
Last edited by Bunuel on 05 Feb 2014, 23:55, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 58340
Re: A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

06 Feb 2014, 00:06
1
1
manish2014 wrote:
A man covers a certain distance in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?

A. 200 km
B. 50 km
C. 20 km
D. 60 km
E. 80 km

(R + 4)(T - 1/2) = (R - 2)(T+1/3).
(R + 4)(T - 1/2) = RT.

Solving gives R = 20 kmh and T = 3 hours. The distance = RT = 60 km.

_________________
Intern
Joined: 25 Aug 2007
Posts: 43
Re: A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

15 Oct 2015, 18:55
Can anybody explain the second equation (R + 4)(T - 1/2) = RT (I understand the first - it is straight of steam) or show a different way to solve?
CEO
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

15 Oct 2015, 19:14
1
inter wrote:
Can anybody explain the second equation (R + 4)(T - 1/2) = RT (I understand the first - it is straight of steam) or show a different way to solve?

Both the equations are from the give information and applying the formula Distance = Speed * Time

(R + 4)(T - 1/2) = (R - 2)(T+1/3) ....(1)

(R + 4)(T - 1/2) = RT.....(2)

R and T are the rate and time taken respectively.

You need to remember that the total distance traveled remains the same. Only the rates (R) and time taken (T) changes.

RT= Distance covered with original rate and time taken

(R + 4)(T - 1/2) = Distance covered with original rate+4 kmph and time taken is original time - 30 minutes.

Equation 2, equates the total distance traveled with 'original conditions' to the total distance covered with modified rates. The total distance remains the same.

Hope this helps.
Intern
Joined: 25 Aug 2007
Posts: 43
Re: A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

15 Oct 2015, 19:30
Thanks a lot. Still, those two systems of equations look rather complex to solve
CEO
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

15 Oct 2015, 19:35
inter wrote:
Thanks a lot. Still, those two systems of equations look rather complex to solve

Not really. When you solve the 2 equation above, you get,

6T-4/3 = 5R/6 from simplifying equation 1

4T-2=R/2 from simplifying equation 2

You can now multiply equation 2 by 5 to get

5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance = R*T=20*3=60 km.

This much of calculation will be required sometimes in GMAT. If you are not comfortable with this, then practice solving algebraic equations.

Hope this helps.
Intern
Joined: 25 Aug 2007
Posts: 43
Re: A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

15 Oct 2015, 19:53
6T-4/3 = 5R/6

Quote:
4T-2=R/2

You can now multiply equation 2 by 5 to get

5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance = R*T=20*3=60 km.

Yep - this is what I call "complex" . I though there might be another shortcut.
Board of Directors
Joined: 17 Jul 2014
Posts: 2514
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

14 Oct 2016, 07:47
manish2014 wrote:
A man covers a certain distance in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?

A. 200 km
B. 50 km
C. 20 km
D. 60 km
E. 80 km

oh man..today i am so slow....

wrote tens of time the same equation and couldn't solve it...what a shame...though it is very simple...

suppose we have R - rate, T-time. RT=distance
(R+4)(T-1/2) = RT
RT - R/2 +4T -2 = RT
-R/2 + 4T -2 = 0 | multiply by 2 everything
-R + 8T - 4 =0 -> R=8T-4

second equation:
(R-2)(T+1/3) = RT
RT +R/3 -2T -2/3 = RT
R/3 -2T -2/3 = 0 | multiply everything by 3
R - 6T - 2 = 0
R=6T+2
now..we have 2 equations for R
8T-4 = 6T+2
2T=6
T=3.
R=6*3+2 = 20

RT = 20 * 3 = 60

D
VP
Joined: 07 Dec 2014
Posts: 1222
A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

14 Oct 2016, 10:47
1
manish2014 wrote:
A man covers a certain distance in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?

A. 200 km
B. 50 km
C. 20 km
D. 60 km
E. 80 km

(r+4)(t-1/2)=r*t=distance
(r-2)(t+1/3)=r*t=distance
[1] 8t-r-4=0
[2] -6t+r-2=0
2t-6=0
t=3
r=20
r*t=20*3=60 km distance
D.
Non-Human User
Joined: 09 Sep 2013
Posts: 13167
Re: A man covers a certain distance in a train. If the train mov  [#permalink]

### Show Tags

03 Mar 2019, 05:04
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 man covers a certain distance in a train. If the train mov   [#permalink] 03 Mar 2019, 05:04
Display posts from previous: Sort by