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Question
A fast train takes 3 hours less than a slow train for a journey of 600kms. If the speed of the slow train is 1 Okm/ hr less than the fast train, find the speed of the fast train.
Solution
Let the speed of the slow train be S, Hence speed of the fast train = S+ 10.
D=600Km, Time = Distance/ Speed. Time difference=3 Hours
Hence, in these two conditions,
`600/"s" - 600/("s" + 10) = 3`
⇒ 600 x (s+ 10) - 600 x S= S x (S+ 10) x 3
⇒ 3s2 + 305 - 6000 = 0
⇒ S2+ 10S - 2000 = 0
⇒ S2 +5O S - 40 s - 2000 = 0
⇒ S (S + 50)- 40 (S + 50 ) = 0
⇒ (S +5O ) (S - 40) = 0
As the speed can't be negative, S=40 km/ hr
Hence, speed of the fast train = 40+ 10 = 50 km/ hr
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