Question

A swimmer can swim at twice the speed of the prevailing tide. If it takes her 4 minutes to swim round trip to a buoy, how long will it take her to swim the identical trip in still water?

Answer 1

I'm pretty sure the answer is 3 minutes, i can show you my work.

Answer 2

let p = rate of prevailing tide
2p = rate of swimmer
t1 = time to swim to buoy
t2 = time to swim back from buoy to beach
d = distance from beach to buoy
Given t1 + t2 = 4
d= (2p+p)* t1
d=(2p - p)*t2
t1 = d/(3p)
t2 = d/p.
d/(3p) + d/p = 4

Answer 3

the last equation gives us
d/(3p) + 3d/(3p) = 4
4d/(3p) = 4
4d = 12p,
So p = d/3.
Now in still water we have
2p*t = 2d ,
t = 2d / (2p)
t = 2d / ( 2*d/3) = 3 minutes

Answer 4

at first my intuition told me the answer should be 4 minutes in still water, because the amount of time the swimmer gained she lost when she swam back?

Answer 5

my intuition still bugs me about this problem

Answer 6

Your intuition is wrong because you might imagine her swimming at the same speed as the current. Now she will never get to the buoy! But somehow if she swims faster than the current her time will somehow magically be the same whether there's a current or not? This is kind of worth it for you to think it through a little more, it wouldn't be as satisfying to just give it away so easily! =D

Answer 7

do you agree with my solution, and why does it take so long... am i making this complicated?

Answer 8

oh in the beginning she is swimming against the tide, (because the tide is coming in?) actually im not sure, does it matter?

Answer 9

if shes smart, she can reach the buoy then wait for the tidal current to change direction

Answer 10

No, I don't think it changes direction. I think if we call her speed 2p and the tide p then going one way the speeds add because it's pushing her along with it:

2p+p

and the other way the speeds subtract

2p-p

since she has to work against the current.

Looks like that's what you did. I'm kind of preoccupied at the moment so I'm not paying much attention sorry.

Answer 11

i know it doesn't change direction, i said if she *waits* it will change direction (like she might have to wait 5 hours)

Answer 12

The strongest tidal currents occur at or around the peak of high and low tides. When the tide is rising and the flow of the current is directed towards the shore, the tidal current is called the flood current, and when the tide is receding and the current is directed back out to sea, it is called the ebb current. Because the relative positions of the moon, sun and earth change at a known rate, tidal currents are predictable.

Answer 13

http://science.howstuffworks.com/environmental/earth/oceanography/ocean-current4.htm

Answer 14

Lol yeah sure, tell your teacher that.

Answer 15

she will probably die of boredom waiting for the tide to change