SOLUTION: Here is my question: A boat travels 12km upstream and back in 3 hours. If the speed of the current is 3 km/h throughout, make an equation and find the speed of the boat in still

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Question 975138: Here is my question:
A boat travels 12km upstream and back in 3 hours. If the speed of the current is 3 km/h throughout, make an equation and find the speed of the boat in still water.
Thank you very much!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
r, boat if no current
c, current
d, distance each way
t, total time up and back

RT=D basic uniform rates travel relationship


__________________speed__________time__________distance
UP________________r-c____________d/(r-c)___________d
BK________________r+c____________d/(r+c)___________d
Total____________________________t____________2d

UNKNOWN VARIABLES: r
KNOWN: c, t, d.

highlight_green%28d%2F%28r-c%29%2Bd%2F%28r%2Bc%29=t%29, and you want to solve for r.

d%28r%2Bc%29%2Bd%28r-c%29=t%28r-c%29%28r%2Bc%29
dr%2Bcd%2Bdr-dc=t%28r%5E2-c%5E2%29
2dr=tr%5E2-tc%5E2
tr%5E2-2dr-tc%5E2=0
You might expect that as an academic exercise, that the trinomial may be factorable, but staying completely in symbols,

r=%282d%2B-+sqrt%284d%5E2%2B4t%2Atc%5E2%29%29%2F%282t%29

r=%282d%2B-+2sqrt%28d%5E2%2Bt%5E2c%5E2%29%29%2F%282t%29

highlight%28r=%28d%2B-+sqrt%28d%5E2%2B%28tc%29%5E2%29%29%2Ft%29
You would want the PLUS form. Substitute the given values for d, t, c, and evaluate r.

Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!

Here is my question:
A boat travels 12km upstream and back in 3 hours. If the speed of the current is 3 km/h throughout, make an equation and find the speed of the boat in still water.
Thank you very much!
Let speed of boat in still water, be S

Time taken to travel upstream: 12%2F%28S+-+3%29

Time taken to travel downstream: 12%2F%28S+%2B+3%29

Therefore, we have: 12%2F%28S+-+3%29+%2B+12%2F%28S+%2B+3%29+=+3

12(S + 3) + 12(S – 3) = 3(S – 3)(S + 3) ----- Multiplying by LCD, (S – 3)(S + 3)

12S+%2B+36+%2B+12S+-+36+=+3%28S%5E2+-+9%29

12S+%2B+12S+%2B+36+-+36+=+3S%5E2+-+27

24S+=+3S%5E2+-+27

3S%5E2+-+24S+-+27+=+0

3%28S%5E2+-+8S+-+9%29+=+3%280%29

S%5E2+-+8S+-+9+=+0

(S - 9)(S + 1) = 0 

S, or speed in still water = highlight_green%289%29 mph	     OR	        S = - 1 (ignore)