Consider two trains A and B such that A takes t hours to cover a stretch of 200 km. Now train B which is 25 km/h faster than A takes 24 min less than A. Find the speeds of the train A and B.

Let the speed of train A = x km/hthen the speed of train B = x+25 km/hTotal distance to be covered = 200 kmTime taken by train A to cover 200 km = t hrs200x = t     .....1Time taken by train B to cover 200 km = t - 2460 hrs = t - 25 hrs200x+25 =t - 25    200x+25 + 25 = t    .....2Now, from 1 and 2, we get200x = 200x+25 + 25200x - 200x+25 = 25200x + 5000 - 200xxx+25 = 252500x2+25x = 15x2 + 25x - 12500 = 0x2 + 125x - 100x - 12500 = 0xx + 125 - 100x + 125 = 0x - 100x + 125 = 0x = 100   or    x = -125 rejectedSo, speed of train A = 100 km/hSpeed of train B = 100+25 km/h = 125 km/h

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let speed of train a be x KM/H

then according to question      x=200/t        (speed = dist/time)
t=200/x

For train B
24min=24/60h=2/5

x+25=200/t-(2/5)

X+25=200/(200/x)-(2/5)
X+25=200/1000-2x/5x
​X+25=500x/500-x
on simplifying we get
12500-x2 -25x =0
-x2-125x + 100x +12500=0
-x(x+125) + 100(x+125)=0
(x+125)(100-x)=0
so x= -125 or x= 100
since speed cannot be negative so x=100
hence speed of train A=100 and speed of train B =100+25=125 KM/H

 
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