SOLUTION: Liz and Mary took a canoeing trip, traveling 6 miles upstream along a river, against a 2 mph current. They returned downstream to the starting point of their trip. If the entire tr

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Question 828691: Liz and Mary took a canoeing trip, traveling 6 miles upstream along a river, against a 2 mph current. They returned downstream to the starting point of their trip. If the entire trip took 4 hours, what was their rate in still water ?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
d = 6
r = canoe speed without current
c = 2, speed of current
T =4, total time

______________speed_____________time______________distance
Going_________r-2_______________(___)_____________6
Return________r+2_______________(___)_____________6
Total____________________________T

What are the missing time parts?


______________speed_____________time______________distance
Going_________r-2_______________(6/(r-2))_____________6
Return________r+2_______________(6/(r+2))_____________6
Total____________________________T

Obvious equation is 6%2F%28r-2%29%2B6%2F%28r%2B2%29=T
6%281%2F%28r-2%29%2B1%2F%28r-2%29%29=T
6%28%28r%2B2%2Br-2%29%2F%28r%5E2-4%29%29=T
6%282r%29%2F%28r%5E2-4%29=T
r%2F%28r%5E2-4%29=T%2F12
r=%28r%5E2-4%29T%2F12 and we already know T=4
r=%28r%5E2-4%29%284%2F12%29
r=%281%2F3%29%28r%5E2-4%29
3r=r%5E2-4
highlight_green%28r%5E2-3r-4=0%29 ------ seems factorable. One solution will make sense and the other will not make sense.


(r-4)(r+1)=0

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Liz and Mary took a canoeing trip, traveling 6 miles upstream along a river, against a 2 mph current. They returned downstream to the starting point of their trip. If the entire trip took 4 hours, what was their rate in still water ? 


Let speed in still water be S

Traveling AGAINST the current, time taken to travel upstream = 6%2F%28S+-+2%29

Traveling WITH the current, time taken to travel downstream = 6%2F%28S+%2B+2%29

Since total time taken for the round trip is 4 hours, then:

6%2F%28S+-+2%29+%2B+6%2F%28S+%2B+2%29+=+4

6%28S+%2B+2%29+%2B+6%28S+-+2%29+=+4%28S+-+2%29%28S+%2B+2%29 ------- Multiplying by LCD, (S - 2)(S + 2)

6S+%2B+12+%2B+6S+-+12+=+4%28S%5E2+-+4%29

6S+%2B+6S+=+4S%5E2+-+16

4S%5E2+-+12S+-+16+=+0

4%28S%5E2+-+3S+-+4%29+=+4%280%29

S%5E2+-+3S+-+4+=+0



Solve to obtain S, or speed of boat, in still water, ACCEPTING the POSITIVE solution, while IGNORING the 

negative solution.



Then do a check!! 



If you need a complete and detailed solution, let me know!!



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