A man crosses a river in a boat. If the crosses the river in minimum time he takes 10 min with a drift 120 m. If he crosses the river taking shortest path, he takes 12.5 min, find
a.width of the river
b. velocity of the boat with respect to water
c. speed of the current.

Explanation

Let `v_(x)=` velocity of river
`v_(br)=` velocity of boat in still water and
w= width off river
Given `t_("min")=10` min or `w/(v_(br))=10` ………I
Drift in this case will be

`x=v_(r)t`
`120=10v_(x)`....ii
Shortest path is taken when `v_(b)` is along AB in this case `v_(b)=sqrt(v_(br)^(2)-v_(r)^(2))`
Now `12.6=w/(v_(b))=w/(sqrt(v_(br)^(2)-v_(r)^(2)))`

Solving these three equations we get `v_(br)=20` m/ min `v_(r)=12` m/min and w=200 m