Q. 34.3( 180 Votes )

# A train covered a

Answer :

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*)

⇒ (x + 10) =

⇒ (x + 10)(t - 2) = d

⇒ xt + 10t - 2x - 20 = d

From (i), we have

⇒ d + 10t - 2x - 20 = d

⇒ - 2*x* + 10*t* = 20

⇒ x - 5t = -10

⇒ x = 5t - 10 (*ii*)

Also,

if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time

⇒ (x - 10) =

⇒ (x - 10)(t + 3) = d

⇒ xt - 10t + 3x - 30 = d

By using equation (*i*),

⇒ d - 10t + 3x - 30 = d

⇒ 3*x* - 10*t* = 30 (*iii*)

Substituting the value of x from eq (ii) into eq (iii), we get

⇒ 3(5t - 10) - 10t = 30

⇒ 5t = 60

⇒

*t*= 12 hours

Putting this in eq(ii)

⇒ x = 5t - 10

= 5(12) - 10

= 50 km/h

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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