26 A ŕ¸ain travels at a certain average speed for a distance of 63

1.	26 A ŕ¸ain travels at a certain average speed for a distance of 63km and the travels a distance of 72 km at anavomge speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, whatis its original average speed?
Answer» Given that distance = 63 km.Let original speed of train = x km/hr.time = distance / time = 63/x hrs. And ittravels a distance of 72 kkm at a average speed of 6 km/hr more than the original speed. distance = 72 km ; speed = (x + 6) km/hr .time = 72/(x+6) hrs.If it takes 3 hours to complete the whole journey63/x + 72/(x + 6) = 3 hrs ⇒ 63(x + 6) + 72x = 3x(x + 6) ⇒ 21(x + 6) + 24x = x(x+6) ⇒ 45x + 21×6 = x^2+ 6x ⇒ x^2- 39x - 126 = 0 ⇒ x^2- 39x - 126 = 0 ⇒ (x - 42)(x + 3) = 0 ∴ x = 42 km/hr∴the original average speed= 42 km/hr

26 A ŕ¸ain travels at a certain average speed for a distance of 63km and the travels a distance of 72 km at anavomge speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, whatis its original average speed?

Answer»

Given that distance = 63 km.Let original speed of train = x km/hr.time = distance / time = 63/x hrs.

And ittravels a distance of 72 kkm at a average speed of 6 km/hr more than the original speed.

distance = 72 km ; speed = (x + 6) km/hr .time = 72/(x+6) hrs.If it takes 3 hours to complete the whole journey63/x + 72/(x + 6) = 3 hrs

⇒ 63(x + 6) + 72x = 3x(x + 6)

⇒ 21(x + 6) + 24x = x(x+6)

⇒ 45x + 21×6 = x^2+ 6x

⇒ x^2- 39x - 126 = 0

⇒ (x - 42)(x + 3) = 0

∴ x = 42 km/hr∴the original average speed= 42 km/hr