Question

a passenger train covers the distance between stations x and y, 50 minutes faster than a goods train. find this distance if the average speeds of the passenger train is 60 kmph and that of goods train is 20

Answer 1

Here we have been given

average speed of passenger train = 60 kmph

average speed of Goods train = 20 kmph

and passenger train covers the distance 50 minutes faster than goods train.

Let 'd' be the distance between the stations X and Y.

Time taken by the passenger train to cover the distance 'd' $= \frac{d}{60} hour$

Time taken by the goods train to cover the distance 'd' $= \frac{d}{20} hour$

Time difference between these two trains is given by 50 minutes or $\frac{50}{60} hour$

i.e ; $\frac{d}{20} - \frac{d}{60} = \frac{50}{60}$

$\frac{60d - 20 d}{20\times60} = \frac{50}{60}$

$\frac{40d}{1200} = \frac{50}{60}$

$40d \times 60 = 1200\times 50$

$2400d =60000$

⇒$d = \frac{60000}{2400}$

⇒ $d = 25 kms$

∴ distance between stations  X and Y is 25 kms.