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

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

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3 months 2021-11-06T17:46:00+00:00 2 Answers 0 views 0

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.

Step-by-step explanation: