A train covered a certain distance …
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A train covered a certain distance at a uniform speed. If the train would have been 10km/h; faster it would take 2 hour less than the scheduled time. And, if the train were slower by 10km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
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Yogita Ingle 5 years, 4 months ago
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=Distance/Time
⇒x= d/t
∴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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