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

Let the time spent traveling by rail be t hours.
Then, the time spent traveling by steamer is (t+8) hours.

We know that:

Distance=Speed×Time
Distance covered by rail:

D
rail
​
=65×t
Distance covered by steamer:

D
steamer
​
=25×(t+8)
The total distance traveled is 434km:

65t+25(t+8)=434
65t+25t+200=434
90t=434−200
90t=234
t=
90
234
​
=2.6hours
Now, find the distance covered by the steamer:

D
steamer
​
=25×(t+8)
D
steamer
​
=25×(2.6+8)
D
steamer
​
=25×10.6=265km