A power boat and a raft both left dock A on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock B downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock A. How many hours did it take the power boat to go from A to B?

Question

anonymous · Answer

let "U" be the speed of the river current
let "v" be the speed of the speedboat
let "L" be the total distance between A and B
let "x" be the total distance from point A to the raft

anonymous · Answer

making the assumption that the raft has not reached point B in 9 hours

anonymous · Answer

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anonymous · Answer

in the 9 hours, the raft only travelled x distance

meaning you can determine speed of the raft/ speed of the river current

anonymous · Answer

in the 9 hours, the speed boat travels from point A - B, then travels from B to the location of the raft
this means the total distance travelled by the speedboat would be L + (L-x)

anonymous · Answer

the speedboat speed when travelling from point A  to point B would be U+V
and the speedboat's speed when travelling upriver would be V-U "making the assumption that the speed of the speedboat is faster than the speed of the current of the river"

anonymous · Answer

let "t1" be the amount of time taken for the speedboat to go from point A to point B


using the knowledge given about the speedboat, you can create 2 equations

L= t1 (U+v)
and 
L-x= (9-t1)( V-U)

the first equation is the distance speed equation for the speedboat as i ts going from point A - point B

the 2nd equation is the distance speed equation for the speedboat going from point B to the position of the raft

at this point, i think its just a bunch of substitution and solving for t1