.
Let "d" be the distance between the points A and B along the river.
Let "u" be the motorboat speed in still water and let "v" be the speed of the current.
Then the effective speed of the motorboat with the current (downstream) is
u + v = (1)
while the effective speed against the current (upstream) is
u - v = . (2)
Subtract equation (2) from equation (1). You will get
2v = = - = .
Hence, v = .
Thus the current speed is units of length per hour.
Now notice, that the motorboat with the engine turned off travels along the river with the effective speed,
EQUAL to the speed of the current.
It means that the motorboat with the engine turned off will cover the distance "d" from A to B in
= 16 hours.
It is the ANSWER to the problem's question: 16 hours.
Solved.
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In order for you better understand the power and beauty of this solution, notice the following:
1) the solution and the answer DO NOT DEPEND on units of length (!).
2) the solution and the answer are valid for any value of "d", the distance between the points (!)
3) The idea of the solution is simple: first find the speed of the current in terms of "d";
then take into account that the speed of the motorboat with the engine turned off is precisely equal
to the speed of the current.
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It is typical problem for the school Math circle level.
In this site, there is a block of lessons on Travel and Distance for upstream and downstream round trips
- Wind and Current problems
- More problems on upstream and downstream round trips
- Wind and Current problems solvable by quadratic equations
- Unpowered raft floating downstream along a river (*)
- Selected problems from the archive on the boat floating Upstream and Downstream
Of these lessons, the lesson marked (*) is exactly and precisely about THIS problem.
Happy learning (!)
Come again to this forum soon to learn something new (!)