SOLUTION: It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A. How many days will it take for a raft to drift from A to B (all spe

Question 1039010: It takes 5 days for a steamboat to travel from A to B along a
river. It takes 7 days to return from B to A. How many days will
it take for a raft to drift from A to B (all speeds stay constant)?
(1) 13
(2) 35
(3) 6
(4) 12
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let the rate of the steamboat be represented by and the rate of the current be represented by . Since the trip from A to B takes less time than from B to A, the boat must be going with the current. That means that the total speed of the boat with respect to the bank of the river is . Likewise, going back upstream, the speed is .

Let represent the distance from A to B. One assumes that A and B are fixed points so that the distance remains constant regardless of the direction of travel. We know that distance equals rate times time, so the downstream trip is modeled by:

and the upstream trip by:

Since , we can write:

Solving:

And substituting into the model for the downstream trip:

Dividing both sides by we get:

And since time is equal to distance divided by rate, we have our answer.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(53763) (Show Source): You can put this solution on YOUR website!
It takes 5 days for a steamboat to travel from A to B along a
river. It takes 7 days to return from B to A.
How many days will
it take for a raft to drift from A to B (all speeds stay constant)?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Also see the lesson Unpowered raft floating downstream along a river in this site, where similar problem was solved.

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