WORD PROBLEM HELP!!!

[turkishpride_69]

Starting at point A, a man rows 1 mile upstream to point B where his hat falls overboard. The man, however, does not notice the loss of the hat and continues rowing upstream. After 10 minutes he realizes that he has lost his hat and immediately turns and rows downstream. Exactly at point A he overtakes his hat, which has been carried downstream by the current. If the man rows at a constant rate relative to the water, what is the rate of the current?

where do i began...is the answer a - b ?

 

[Guest]

need to start by defining some of the distances and velocities.

Let the boat velocity = v
let the current velocity = c
let the distance travelled in the extra 10 min's be x

for the boat
velocity = distance / time

v = x / (10/60) ----this keeps velocity in mph ie 10 mins= 10/60 hour

x= (1/6) v
This is the extra distance the boat goes.

Now work out the time the boat needs to take to travel back a distance of 1+x (the original mile plus the extra x where x= (1/6) v )

This time is also equal to the hat travelling the 1 mile at a velocity of c

time = distance /velocity


have a go with this.....

 

[TchrWill]

Starting at point A a man rolls one mile upstream against
the current to point B his hat falls overboard. The man
doesnt notice the loss of his hat and continues running
upstream after 10 minutes he realizes he has lost his hat
and immediately turns and goes down stream. Exactly at
point A he over takes his hat which has been carried
downstream by the cureent. If the man rolls at the constant
state relative to the water what is the rate of the current?


I<-------10 min------------>I<--------------1 mile------------------->I
0-------------------------------0------------------------------------------0
C.............D.................... B.....................................................A

1--Let Vb = speed of boat and Vc = speed of current or hat.
2--Distance BC = D
3--D = (Vb - Vc)/6 or 6D = (Vb - Vc)
4--1/Vc = 1/6 + (D + 1)/(Vb + Vc) or
5--1/Vc = (Vb + Vc + 6D + 6)/(6(Vb + Vc))
6--6(Vb + Vc)/Vc = Vb + Vc + Vb - Vc + 6 = 2Vb + 6
7--6Vb/Vc + 6 = 2Vb + 6
8--6Vb = 2VbVc
9--Vc = 3 mph

 

[Denis]

Well, why not me too! Borrowing apm's letters:
Let the boat velocity = v mph
let the current or hat velocity = c mph

When boat turns around, boat is 1 + (v - c)/6 from A, and will be travelling at (v + c) mph;
at that point, hat is 1 - c/6 from A, and will keep travelling at c mph.

[1 + (v - c)/6] / (v + c) = (1 - c/6) / c
Solve to get c = 3