The distance travelled by a train is 1830 km. The speed of the train is one more than twice the time taken to travel the distance. What will be the respective ratio of the speed of the train and time taken to travel?

Let time taken to cover the distance = t
∴ Speed = (2t + 1)
⇒ t(2t + 1) = 1830 ⇒ 2t² + t = 1830
⇒ 2t² + t - 1830 = 0
∴ t = -1 ± √(1)² - 4 x 2 x(-1830) / 2 x 2
= -1 ± √1 + 14640 / 4
= -1 ± 121 / 4
Taking '+' sign t = -1 + 121 / 4 = 120/4 = 30
∴ Required ratio = (2 x 30 + 1) : 30 = 61 : 30