Question 22105
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Answer: <font color=red>1/2 of an hour</font> or <font color=red>30 minutes</font>


Explanation


Let's say the river flows south.
Define points A, B, and C such that:
A = log's starting location
B = Phil's starting location
C = point in between A and B where Phil reaches the log
{{{
drawing(300,300,-10,10,-10,10,
line(0,5,0,-7),
circle(0,3,0.2),circle(0,3,0.25),circle(0,3,0.3),
circle(0,-1,0.2),circle(0,-1,0.25),circle(0,-1,0.3),
circle(0,-4,0.2),circle(0,-4,0.25),circle(0,-4,0.3),

line(4,2,4,-5),line(4,-5,3.65,-4.3938),line(4.05,-5,4.4,-4.3938),

locate(0.4,4.2,"A"),
locate(0.4,-1.8+0.8,"C"),
locate(0.4+0.1,-3.8,"B"),
locate(4.5,0,matrix(1,2,"river","flow")),
locate(-9,-9,matrix(1,4,"Diagram","not","to","scale"))
)
}}}
The diagram is optional but could be handy.



Phil's speed is 8 mph in still water.
But since Phil has to swim upstream against the 2 mph current, it slows him down to 8-2 = 6 mph.
So he travels 6x miles where x is the length of time in hours.
I'm using the formula: <pre>distance = rate*time</pre>Meanwhile, the log travels at 2 mph for the same amount of time x.
It travels 2x miles.



To recap so far we have these distances
AC = 2x
BC = 6x


These two distance subtotals must add to the 4 mile gap between the points A and B.
AC+BC = AB
2x+6x = AB
2x+6x = 4
8x = 4
x = 4/8
x = <font color=red>1/2 of an hour</font> aka <font color=red>30 minutes</font>
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