Question

a boat takes 8 hours to go 6 miles upstream and come back to the starting point. if the speed of the boat is 4 miles per hour in still water, what is the rate of the current?

Answer 1

Consider this option:
1. if to re-write the condition, it is given: total time t=8 hours; upstream=downstream=6 miles; V_boat=4 m/h., V_current=V=?
2. note, that total time=time_upstream+time_downstream, where time_upstream=6miles/(V_boat-V) and time_downstream=6miles/(V_boat+V). Using this it is possible to make up and solve the following equation:

`(6)/(4+V) + (6)/(4-V) =8; \ =\ \textgreater \ \ (V^2-10)/(16-V^2)=0; \ =\ \textgreater \ \ V=√(10) \ (miles)/(hour)`

answer: √10

P.S. the roots of the equation are √10 and (-√10), only positive values is needed for V.