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

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manish2014
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A man covers a certain distance in a train. If the train mov [#permalink] New post   Updated on: 05 Feb 2014, 23:55
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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
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D

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.
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Re: A man covers a certain distance in a train. If the train mov [#permalink] New post   06 Feb 2014, 00:06
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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.

Answer: D.
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Re: A man covers a certain distance in a train. If the train mov [#permalink] New post   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?
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A man covers a certain distance in a train. If the train mov [#permalink] New post   15 Oct 2015, 19:14
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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.
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Re: A man covers a certain distance in a train. If the train mov [#permalink] New post   15 Oct 2015, 19:30
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Thanks a lot. Still, those two systems of equations look rather complex to solve
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A man covers a certain distance in a train. If the train mov [#permalink] New post   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.
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Re: A man covers a certain distance in a train. If the train mov [#permalink] New post   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.
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Re: A man covers a certain distance in a train. If the train mov [#permalink] New post   14 Oct 2016, 07:47
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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
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A man covers a certain distance in a train. If the train mov [#permalink] New post   14 Oct 2016, 10:47
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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
adding [1] and [2],
2t-6=0
t=3
r=20
r*t=20*3=60 km distance
D.
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Re: A man covers a certain distance in a train. If the train mov [#permalink] New post   15 Nov 2021, 23:19
Hello from the GMAT Club BumpBot!

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Re: A man covers a certain distance in a train. If the train mov [#permalink]
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