SOLUTION: the current in a river moves at 2mph. a boat travels 18 mph upstream and 7mph down stream in a total 7 hours. what the speed of the boat in still water?
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Question 206290: the current in a river moves at 2mph. a boat travels 18 mph upstream and 7mph down stream in a total 7 hours. what the speed of the boat in still water? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! I assume when you say 18 mph you mean 18 miles, and 7 mph mean 7 miles.
:
the current in a river moves at 2mph. a boat travels 18 miles upstream
and 7 miles down stream in a total 7 hours.
what the speed of the boat in still water?
;
Let s = speed of the boat in still water
then
(s+2) = speed downstream
and
(s-2) = speed upstream
;
Write a time equation: Time =
:
Time downstream + time upstream = 7 hrs + = 7
:
Multiply equation by (s+2)(s-2)
(s+2)(s-2)* + (s+2)(s-2)* = 7*(s+2)(s-2)
:
Cancel the denominators and you have:
18(s-2) + 7(s+2) = 7*(s^2 - 4)
:
18s - 36 + 7s + 14 = 7s^2 - 28
:
25s - 22 = 7s^2 - 28
:
Arrange as a quadratic equation on the right
0 = 7s^2 - 25s - 28 + 22
:
7s^2 - 25s - 6 = 0
:
Use the quadratic formula to find s
In this problem x = s; a = 7; b = -25; c = -6
:
:
:
The positive solution is what we want here
s =
s ~ 3.8 mph in still water
:
:
That is awful slow, let's see if that's true
Upstream time + downstream time = + =
3.89 + 3.10 = 6.99 ~ 7 hrs
