Question

The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.

Answer 1

Let the speed of express train is x
Km/hr. Speed of ordinary train is (x - 12) km/hr.
Time require to cover for each train is `(240)/x` and `(240)/(x - 12)` respectively.
According to question
`(240)/(x - 12) - (240)/x = 1`
`(240x - 240 (x - 12))/((x - 12) (x)) = 1`
240x - 240 (x - 12) = x (x - 12)
x² - 12x - 2880 = 0
(x - 60) (x + 48) = 0
∴ x = 60 km/hr.
Speed of the express train is 60 km/hr.

Answer 2

Let the speed of express train = x km
Then speed of the ordinary train = (x – 12)km
Time is taken to cover 240km by the express

train = `(240)/x"hours"`

Time taken to cover 240km by the ordinary

train = `(240)/(x - 12)"hours"`

According to the condition,

`(240)/(x - 12) - (240)/x` = 1

⇒ `240[(1)/(x - 12) - (1)/x]` = 1

⇒ `240[(x - x + 12)/(x(x - 12))]` = 1

⇒ `240[(12)/(x^2 - 12x)]` = 1

⇒ 2880 = x² - 12x
⇒ x² - 12x - 2880 = 0
⇒ x² - 60x + 48x - 2880 = 0
⇒ x(x  - 60) + 48(x - 60) = 0
⇒ (x - 60)(x + 48) = 0
⇒ x = 60 or x = -48
⇒ x = 60  ...(Rejacting x = -48, as speed can't be negative)
Hence, speed of the express train = 60km/h.