Question

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours and 30 minutes. But, if he travels 260km by train and 240km 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 = 1/40`
⇒ y = 80
Hence, the speed of the train and that of the taxi are 100 km/h and 80 km/h respectively.