A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Let the
speed of the train be *x* km/h and the time taken by train to
travel the given distance be *t* hours and the distance to
travel was *d* km. We know that,

Or, *d =
xt* (*i*)

Using the information given in the question, we obtain

By using
equation (*i*), we obtain

−
2*x* + 10*t* = 20 (*ii*)

By using
equation (*i*), we obtain

3*x*
− 10*t* = 30 (*iii*)

Adding
equations (*ii*) and (*iii*), we obtain

*x* =
50

Using
equation (*ii*), we obtain

(−2)
× (50) + 10*t* = 20

−100
+ 10*t* = 20

10*t*
= 120

*t *=
12 hours

From
equation (*i*), we obtain

Distance
to travel = *d* = *xt*

= 50 × 12

= 600 km

Hence, the distance covered by the train is 600 km.

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