A train covers a distance of 480 km at a uniform speed. If the speed h

1.	A train covers a distance of 480 km at a uniform speed. If the speed had been 8km/hr less, then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.
Answer» Total distance is S = 480 km. Let the speed of the train is x km/hour. ∴ Time taken to cover the distance 480 km is t = \(\frac{480}{x}\) hours … (1) Given that if speed of the train is decreasing by 8 km/hour, it take 3 more hours to cover the same distance. ∴ t +3 = \(\frac{480}{x\, - \,8}\) ⇒ \(\frac{480}{x}+3=\frac{480}{x\,-\,8}\) (By putting the value of t) ⇒ 480(x – 8 – x) + 3x (x –8) = 0 ⇒ 3x (x – 8) = 480 × 8 ⇒ x (x – 8) = 160 × 8 = 1280. ⇒ x² – 8x – 1280 = 0 ⇒ x² – 40x + 32x – 1280 = 0 ⇒ x (x – 40) + 32 (x – 40) = 0 ⇒ (x + 32)(x – 40) = 0 ⇒ x = –32 or x = 40 ⇒ x = 40. (∵ Speed never be negative) Hence, usual speed of the train is 40 km / hour.

A train covers a distance of 480 km at a uniform speed. If the speed had been 8km/hr less, then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

Answer»

Total distance is S = 480 km.

Let the speed of the train is x km/hour.

∴ Time taken to cover the distance 480 km is t = \(\frac{480}{x}\) hours … (1)

Given that if speed of the train is decreasing by 8 km/hour, it take 3 more hours to cover the same distance.

∴ t +3 = \(\frac{480}{x\, - \,8}\)

⇒ \(\frac{480}{x}+3=\frac{480}{x\,-\,8}\) (By putting the value of t)

⇒ 480(x – 8 – x) + 3x (x –8) = 0

⇒ 3x (x – 8) = 480 × 8

⇒ x (x – 8) = 160 × 8 = 1280.

⇒ x² – 8x – 1280 = 0

⇒ x² – 40x + 32x – 1280 = 0

⇒ x (x – 40) + 32 (x – 40) = 0

⇒ (x + 32)(x – 40) = 0

⇒ x = –32 or x = 40

⇒ x = 40. (∵ Speed never be negative)

Hence, usual speed of the train is 40 km / hour.

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