SOLUTION: A boat travels between two cities that are 11 miles apart. When going downstream, with the current, the trip takes 11/17 hour(s). Returning upstream, against the current, the boat

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Question 1185095: A boat travels between two cities that are 11 miles apart. When going downstream, with the current, the trip takes 11/17 hour(s). Returning upstream, against the current, the boat covers the same distance in 11/15
hour(s).
What is the current of the river?
What is the speed of the boat in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A boat travels between two cities that are 11 miles apart.
When going downstream, with the current, the trip takes 11/17 hour(s).
Returning upstream, against the current, the boat covers the same distance in 11/15 hour(s).
:
Let s = speed of the boat in still water
let c = the rate of the current
then
(s+c) = speed downstream
and
(s-c) = speed upstream
:
Write a two dist equations, dist = time * speed
11%2F17(s+c) = 11
11%2F15(s-c) = 11
:
s + c = 11 * 17%2F11
s + c = 17
and
s - c = 11 * 15%2F11
s - c = 15
Use elimination
s + c = 17
s - c = 15
-------------addition eliminates c, find s
2s + 0 = 32
s = 32/2
s = 16 mph is the boat speed in still water
:
find the current
16 + c = 17
c = 17 - 16
c = 1 mph is the current
:
:
Check the solutions in the equation:11%2F17(s+c) = 11
11%2F17(16+1) = 11
11%2F17(17) = 11
17 cancels
11 = 11