Question

A train is running at a uniform speed to cover the distance between two cities. If the
train had been 30 km/h faster, it would have taken 12 hours to complete the journey.
If the train had been 8km/h slower, it would have taken 18 hours to complete the
journey. Find
a. the speed of the train. b. the length of the journey.
​

Answer 1

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

Answer 2

Answer:

Let the speed of train be v

Speed =Distance/time

Distance = speed ×time

Let the distance be x

A/Q

x = (V+30) ×12 ----------------- (i)

and x = (V-8)×18----------------------(ii)

From equation ( i ) and (ii) we have

(V+30)×12= (V-8)×18

12V+360=18V-144

360+144=18V-12V

504=6V

V=504/6

V=84

Therefore the speed of train =84km/h

By putting V=84 in equation (i) we have

x=(84+30)×12

x=144×12

x=1368

Therefore the length of journey=1368km