Question

A train covered a certain distance at a uniform speed if the train had been 30 km per hour faster it would have taken 2 hours less than the scheduled time if the train was lowered by 15 km per hour it would have taken 2 hours more than the scheduled time find the length of the journey

Answer 1

Let the speed of the train by x km/hr
And the time taken by the train be ‘y’ hrs
Distance traveled by the train is x.y = xy

Case I
If the train would have been 30 km/hr faster, it would have taken 2 hours less than the scheduled time.
⇒ (x + 30) (y - 2) = 60

Case II
If the train were slower by 15 km/hr, it would have taken 2 hours more than the scheduled time
⇒ (x - 15) (y +  2) = 30

Solve the (1) and (2) equation and multiply x * y
then , you will get your answer

Answer 2

Answer:

Let the speed of the train be xkm/h and the time taken by train to travel the given distance be t hours and the distance to travel be dkm. We know that,

⇒Speed= Time/Distance

⇒x= t/d

∴d=xt.......(i)

Case 1

⇒(x+10)×(t−2)=d

⇒xt+10t−2x−20=d

⇒d+10t−2x−20=d

⇒−2x+10t=20...... (ii)

Case 2

⇒(x−10)×(t+3)=d

⇒xt−10t+3x−30=d

⇒d−10t+3x−30=d

⇒3x−10t=30......... (iii)

Adding equations (ii) and (iii), we gets

⇒x=50

Substitute the value of x in (ii) we gets

⇒(−2)×(50)+10t=20

⇒−100+10t=20

⇒10t=120

⇒t=12 hours

Substitue the value of t and x in equation (i), we gets

Distance to travel =d=xt

⇒d=12×50=600Km

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