Two boats, `A` and `B`, move away from a point `P` at the middle of a river along the mutually perpendicular straight lines. Boat `A` moves along the river and boat `B` across the river. Having moved off equal distance from point `P` the boats returned. find the ratio of times of motion of boats `(t_(A))/(t_(B))` if `v=etau(etagt1)`. (`v` : velocity of boat with respect to water. `u`: stream velocity)

Explanation

Boat `A: t_(A)=d/(v-u)+d/(v+u)=(2dv)/(v^(2)-u^(2))`
Boat `B: t_(B)=(2dv)/(sqrt(v^(2)-u^(2)))` (as in Example 13)
`(t_(A))/(t_(B))=v/(sqrt(v^(2)-u^(2)))=(etau)/(sqrt((etau)^(2)-u^(2)))=(eta)/(sqrt(eta^(2)-1))`