If a train runs at 40 kmph it reaches its destination late by 11 minutes. But if it runs at 50 kmph it is late by 5 minutes only. Find the distance covered by the train.
Let the correct time for the train to complete the journey be x hours
Time taken by train if it runs at 40 kmph=x hours 11 minutes=(x+1160) hours
So, distance covered by train if it runs at 40 kmph
=40×(x+1160) km [Distance = Speed × Time] ------- (1)
Time taken by train if it runs at 50 kmph=x hours 5 minutes=(x+560) hours
So, the distance covered by train if it runs ar 50 kmph
=50×(x+560) km ------ (2)
Since both distances are equal.
40×(x+1160)=50×(x+560) [From (1) and (2)]
⇒40×(60x+1160)=50×(60x+560)
⇒40(60x+11)=50(60x+5)
⇒2400x+440=3000x+250
⇒440−250=3000x−2400x
⇒600x=190
⇒x=190600
⇒x=1960 hours
⇒x=1960×60 minutes
⇒x=19 minutes
From eq (1),
Distance = 40×(x+1160) km
=40×(1960+1160) km [∵x=19]
=40×19+1160 km
=40×3060 km
=40×12 km
=20 km
Therefore, the distance covered by train is 20 km.