SOLUTION: please explain this problem step by step. I am very confuse. seting up an equation in two variables for each problme. then solve. A rowing team rowing with the current traveled 18

Question 276379: please explain this problem step by step. I am very confuse. seting up an equation in two variables for each problme. then solve. A rowing team rowing with the current traveled 18 mi in 2h. against the curret, the team rowed a distance of 8 mi in the same amount of time. find the rate of the rowing team in calm water and rate of the curreent. PLEASE HELP
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rowing team rowing with the current traveled 18 mi in 2h.
against the current, the team rowed a distance of 8 mi in the same amount of time.
find the rate of the rowing team in calm water and rate of the current
:
Let r = the rowing rate in still water
Let c = rate of the current
then
(r+c) = speed downstream
and
(r-c) = speed upstream
:
Write a distance equation for each way. Dist = speed * time (2hrs for both)
2(r+c) = 18; (downstream)
2(r-c) = 8: (upstream)
;
Multiply what's inside brackets in both equations, then use elimination:
2r + 2c = 18
2r - 2c = 8
----------------adding eliminates c, find r
4r + 0c = 26
4r = 26
r =
r = 6.5 mph rowing speed in still water
:
Find c using the equation 2r + 2c = 18, substitute 6.5 for r
2(6.5) + 2c = 18
13 + 2c = 18
2c = 18 - 13; subtract 13 from both sides
2c = 5
c =
c = 2.5 mph is the rate of the current
:
:
Check solutions in the original upstream equation, substitute for r and c
2(r-c) = 8:
2(6.5 - 2.5) = 8
2(4) = 8; confirms our solution
:
:
Did this unconfuse you, any questions, ankor@att.net
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