SOLUTION: A boat travels 80 miles upstream in a river with a current of 6 miles per hour; then it travels back down to its starting point. The total time of the trip was 4 hours. Find the

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Question 375325: A boat travels 80 miles upstream in a river with a current of 6 miles per hour; then it travels back down to its starting point. The total time of the trip was 4 hours. Find the speed of the boat in still water. what is the equation too?
Found 2 solutions by Jk22, mananth:
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
let
v>0 speed of the boat in still water, tup, time upstream

upstream travel : 80 = (v-6)*tup
downstream : 80 = (v+6)*tdown

tup+tdown = 80/(v-6)+80/(v+6) = 4


80(v+6)+80(v-6) = 4(v^2-36)

40v = v^2 - 36 => v^2 - 40v - 36 = 0 = (v - 20)^2 - 400 - 36

(v-20)^2 = 436 = 218*2 = 109*4

v = 20 + 2Sqrt(109) mph

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let speed of boat in still water be x mph
..
current speed = 6 mph.
..
speed upstream = x-6 mph
speed downstream = x+6 mph.
..
t = d/r
time upstream + time downstream = 4 hours
80%2F%28x-6%29%2B80%2F%28x%2B6%29+=4
..
%2880%2A%28x%2B6%29%2B80%2A%28x-60%29%29%2F%28%28x%2B6%29%2A%28x-6%29%29=4
...
%2880x%2B480%2B80x-480%29%2F%28%28x%2B6%29%28x-6%29%29=4
...
%28160x%29%2F%28%28x%2B6%29%28x-6%29%29=4
...
multiply by (x+6)(x-6)

..
160x= 4x^2-36
4x^2-160x-36=0
/4
x^2-40x-9=0
discriminant = 1636
x1=((40+sqrt(1636)))/2
x1=40.2 mph speed of boat in still water
x2 will be negative so ignore
...
m.ananth@hotmail.ca