Answer to Question #251188 in Mechanics | Relativity for drake

Question

A boat moving downstream (with the current) in a river takes 4 min and 7secs to cover

a measured mile according to marks on shore, and 7 min and 30 secs to cover the same

distance moving upstream (against the current). If the boat’s velocity relative to the

water is 11 km/h, what is the velocity of the current in the river?

Answer 1

Express the time of motion downstream and upstream:

$$t_d=\frac{d}{v+u},\\\space\\ t_u=\frac{d}{v-u},\\\space\\ t_dv+t_du=t_uv-t_uu,\\\space\\ u=v\frac{t_d-t_u}{t_d+t_u}=1.24\text{ km/h}.$$