Question

A train covers a certain distance at a uniform speed . On increasing its speed by 5 km/hr it saves 20 minutes and on decreasing its speed by 20 km/hr it loses 2 hrs. Find the distance covered by the train

Answer 1

Step-by-step explanation:

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.

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Answer 2

Answer:

Step-by-step explanation:

Answer:

Let us consider

Time is taken = t

Speed = x

Distance = d

Time = Distance/Speed

or

Speed = Distance/time

x = d/t

d = xt………………………………….(1)

Case 1:

d = (x + 10)(t – 2)

d = xt – 2x +10t -20

d = d – 2x +10t -20 [from (1) xt = d]

10t – 2x = 20…………………………………..(2)

Case2:

d = (x – 10)(t + 3)

d = xt + 3x -10t – 30

d = d + 3x -10t – 30 [from (1) xt = d]

3x -10t = 30…………………………………..(3)

Adding equation (2) and (3)

(10t – 2x + 3x -10t) = 20 + 30

x = 50

Substituting the value of x in 2

10t – 2 × 50 = 20

10t = 100 + 20

10t = 120

t = 12 hours

Now substitute the value of t and in x in equation (1)

Distance d = xt

d = 50 × 12

d = 600 km

Therefore distance covered by the train is 600km.