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It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours.
How long does it take an unpowered raft to cover this distance?
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Raft (see this article of Wikipedia)
A raft is any flat structure for support or transportation over water. It is the most basic of boat design,
characterized by the absence of a hull. Although there are cross-over boat types that blur this definition,
rafts are usually kept afloat by using any combination of buoyant materials such as wood, sealed barrels,
or inflated air chambers (such as pontoons), and are typically not propelled by an engine.
It is assumed in this problem that the unpowered raft moves along the river with the current' speed.
Therefore, all we need to do is to determine the speed of the current.
Let D be the distance along the river from pier A to pier B.
Let "u" be the motorboat speed in still water and "v" be the current speed.
When moving upstream, the motorboat has the speed u-v (relative to the river's banks), and it is equal to .
When moving downstream, the motorboat has the speed u+v (relative to the river's banks), and it is equal to .
So, you have these two equations
u + v = , (1)
u - v = . (2)
Distract equation (2) from equation (1) (both sides). You will get
2v = = = = .
Hence, v = = .
Now, the time for the unpowered raft to cover the distance D is
= = 192 hours.
Answer. The time for the unpowered raft to get from pier A to pier B is 192 hours.