Question

A man travels 434 km in, partly by rail and partly by steamer. he spends 8 hours more time on steamer. if the velocity of the steamer is 25 km/hr and the velocity of rail is 65 km/hr, how much distance does he cover by steamer?

Answer 1

Total distance = 434km

time spent on rail = x hrs

time spent on steamer = (x+8) hrs

steamer vel = 25km/hr; dist = vel x time = 25 x (x+8) km

rail vel = 65km/hr; dist = vel x time = 65 x (x) km

Acc. to que,

 25 x (x+8) km   +   65 x (x) km  =   434 km

or, 25x + 200 + 65x = 434

or, 90x + 200 = 434

or, 90x = 434 - 200

or, 90x  = 234

or, x = 2.6 hrs = 2 hrs 36 mins.(Ans)

Now, distance covered by steamer = 25 x (2.6 + 8)
                                                        = 25 x 10.6
                                                        = 265 km.

For dist travelled by rail = 434 - 265

                                      = 169 km.