Question
A train covers a route at its usual speed. If it had
gone 20 km/h faster, it would have taken 4 hours less. If it had gone 20 km/h slower, it would have taken 12 hours more. Find the train’s usual speed.Solution
Let distance = d km, speed = s km/h, time = t h. (I) d = s·t Faster by 20: (II) d = (t − 4)(s + 20) From (I) & (II): s·t = (t − 4)(s + 20) ⇒ s·t = s·t − 4s + 20t − 80 ⇒ 20t − 4s = 80 … (III) Slower by 20: (IV) d = (t + 12)(s − 20) From (I) & (IV): s·t = (t + 12)(s − 20) ⇒ s·t = s·t + 12s − 20t − 240 ⇒ 12s − 20t = 240 … (V) Add (III) and (V): (20t − 4s) + (12s − 20t) = 80 + 240 ⇒ 8s = 320 ⇒ s = 40 Hence, usual speed = 40 km/h.
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