Question

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours and 30 minutes. But, if he travels 260 km by train and 240 km by taxi, he takes 6 minutes longer. Find the speed of the train and that of taxi.

Answer 1

Let the speed of the train and taxi be x km/h and y km/h respectively.

Then as per the question

`3/x + 2/y = 11/200`   ...(i)

When the speeds of the train and taxi are 260 km and 240 km respectively, then

`260/x + 240/y = 11/2 + 6/60`

⇒ `13/x + 12/y = 28/100`   ...(ii)

Multiplying (i) by 6 and subtracting (ii) from it, we get

`18/x - 13/x = 66/200 - 28/100`

⇒ `5/x = 10/200`

⇒ x = 100

Putting x = 100 in (i), we have

`3/100 + 2/y = 11/200`

⇒ `2/y = 11/200 - 3/100`

⇒ `2/y = 1/40`

⇒ y = 80

Hence, the speed of the train and that of the taxi are 100 km/h and 80 km/h respectively.