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
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-> 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
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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):
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
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)?
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