A train covered a certain distance at a uniform speed. If the train would have been6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if thetrain were slower by 6 km/h; it would have taken 6 hours more than the scheduledtime. Find the length of the journey

Let's denote:

• The original speed of the train as 's' (in km/h)
• The original time it took as 't' (in hours)
• The distance of the journey as 'd' (in km)

From the problem, we know that speed = distance/time. So, we can write the distance 'd' as:

1. d = s*t

We also know that if the train were 6 km/h faster, it would have taken 4 hours less. So, we can write:

2. d = (s+6)(t-4)

And if the train were 6 km/h slower, it would have taken 6 hours more. So, we can write:

3. d = (s-6)(t+6)

Now, we have three equations with three unknowns (d, s, t). We can solve these equations simultaneously to find the values of d, s, and t.

From equation 1) and 2), we get:

st = (s+6)(t-4) => st = s*t + 6t - 4s - 24 => 4s = 6t - 24 => 2s = 3t - 12 ----(4)

From equation 1) and 3), we get:

st = (s-6)(t+6) => st = s*t + 6s - 6t - 36 => 6s = 6t - 36 => s = t - 6 ----(5)

Now, we can solve equation 4) and 5) to find the values of s and t:

Substitute equation 5) into equation 4):

2(t - 6) = 3t - 12 => 2t - 12 = 3t - 12 => t = 12

Substitute t = 12 into equation 5):

s = 12 - 6 = 6

Finally, substitute s = 6 and t = 12 into equation 1) to find the distance 'd':

d = 6 * 12 = 72 km

So, the length of the journey is 72 km.