# A train covered a certain distance at a uniform speed. If the train would have been 6km/hr. faster, it would have taken 4 hours less than the scheduled time. And if the train were slower by 6km/hr. it would have taken 6 hours more than the scheduled time. Find the length of the journey.

let the speed of the train = x km/hr

let the distance covered = y km.

scheduled time to cover the distance = distance / speed

= y / x hr

if the train is 6 km / hr faster, new speed = (x+6) km/hr

it would have taken 4 hr less, therefore if the train were 6 km / hr slower, new speed = (x-6) km / hr

it would have taken 6 hrs more, therefore substituting the value of y in terms of x , from eq(2) to eq(1):  since x is the speed of the train therefore x =30 km / hr

and substitute x = 30 in eq(2): thus the distance covered is 720 km and speed of the train is 30 km / hr.

hope this helps you.

cheers!!

• 148

let the actual speed of the train be x & actual time taken be y

distance covered = xy  ....(1) {distance = speed * time}

if the speed is increased by 6km/hr & time of journey is reduced by 4hrs i.e. when speed =(x + 6) & time of journey =(y - 4)

distance covered = (x + 6) (y - 4)

xy = (x + 6) (y - 4)  {using eq (1)}

-4x+ 6y - 24= 0

-2x + 3y = 12  ....(2)

when the speed is reduced by 6km/hr & time of journey is increased by 6hrs i.e. when speed = (x - 6) & time of journey = (y + 6)

distance covered = (x - 6) (y + 6)

xy = (x - 6) (y + 6)  {using eq (1)}

6x - 6y - 36 = 0

x - y = 6  ....(3)

thus we obtain the following set of eq.

-2x + 3y = 12

x - y = 6

by substitution method

x = 6+ y  ....(4)  {from eq (3)}

from eq (2) & (4)

-2(6 + y) + 3y = 12

-12 -2y + 3y = 12

y = 24

x = 6 + 24  { from eq (4)}

x = 30

hence distance covered = xy = 30 * 24 = 720 km

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