"Do not wait for leaders; do it alone, person to person."
- Mother Teresa
28.
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:
(A's speed) : (B's speed) = (b : a)
Deepika said:
(Thu, Jan 20, 2011 08:51:29 AM)
Please explain me only the last step.
Gowthami said:
(Fri, Feb 25, 2011 02:33:03 PM)
Hi Deepika
The last step is converting m/sec to km/hr.
But i am not understanding how can the dist be equated?
(x - 1.25) x 8.4 = (x - 1.5) x 8.5
can any one explain it plz.
Gowthami said:
(Tue, Jun 7, 2011 07:33:00 AM)
@Gowthami
4.5km/hr=4.5x5m/sec =5m/sec=1.25m/sec
5.4km/hr=5.4x5m/sec=3m/sec=1.5m/sec
then speed of the train=x
distance=speed*time
so distance=(x-1.25)*8.4-------------1
distance=(x-1.5)*8.5----------------2
(1)=(2)
(x - 1.25) x 8.4 = (x - 1.5) x 8.5
Manasa said:
(Sun, Jun 12, 2011 06:51:42 AM)
There is no need of confusion regarding this problem.
in this problem...train and the two persons are moving in the same direction...
Consider the speed of the train be X km/hr.
**(note:the SPEED and LENGTH remains same in both the cases)****
----------------------------------------------------------------
now let us consider relative speed of the train w.r.to the first person..we get...(X-1.25)
in similar manner,relative speed w.r.to the second train...we get...(X-1.5)
(NOTE:why i'm doing subtraction here ,since they are moving in the same direction)
now we know,distance=speed*time
(x - 1.25) x 8.4 = (x - 1.5) x 8.5
8.4x - 10.5 = 8.5x - 12.75
0.1x = 2.25
x = 22.5
speed of the train=22.5 * (5/18)=81km/hr
Swetha said:
(Wed, Aug 3, 2011 04:02:51 PM)
Good explanation. Thank you manasa.
Vinay said:
(Thu, Aug 18, 2011 10:52:13 AM)
But as manasa said why to equal both the relative speed's.
I am not understanding. Can any one please help me.
Gururaj said:
(Fri, Sep 16, 2011 11:57:12 PM)
But the two man is also moving then there is change in distance, so how then (x-1.25)x8.4=(x-1.5)x8.5 both are moving so both the distance are varying.
Can some one please explain this?
Vinay Rawat said:
(Mon, Oct 17, 2011 11:52:41 AM)
How can we assume that the distance is equal ?
Krishna said:
(Wed, Nov 30, 2011 10:29:21 PM)
Distance means it,s length of train ---------->(x-1.25)*8.4
(x-1.25)------>is relative speed,
8.4----------->time.
Same as in case of (x-1.5)x8.5.
In both cases gives distence of cover it,s idirectly both are same.
So (x-1.25)x8.4=(x-1.5)x8.5-----> find x from this you can get speed
Kishore Mech said:
(Thu, Jan 26, 2012 06:13:27 PM)
x is the length of the train; y is the velocity of the train
x/y=t1 ; x/y=t2
x/(y-1.25)=8.4 ; x/(y-1.5)=8.5
[4.5kmph=1.25m/s ;5.4kmph=1.5m/s]
x-8.4y=-10.75..........(1)
x-8.5y=-12.75..........(2)
solving the equ 1 & 2
we get thge solution y=22.5m/s
there for ans;
the speed of the train y=22.5m/s=81kmph
Yaswanth said:
(Sat, Feb 11, 2012 12:00:38 PM)
Hi Vinay, the distance here is the length of train.... Consider the human as a point. Then length of train from case 1 is 8.4(x-1.25) and from case 2 is 8.5(x-1.5)...
8.4x - 10.5 = 8.5x - 12.75
Speed of the train =