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

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) (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.

, and you want to solve for r.

You might expect that as an academic exercise, that the trinomial may be factorable, but staying completely in symbols,

You would want the PLUS form. Substitute the given values for d, t, c, and evaluate r.
Answer by MathTherapy(10810) (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:
Time taken to travel downstream:
Therefore, we have:
12(S + 3) + 12(S � 3) = 3(S � 3)(S + 3) ----- Multiplying by LCD, (S � 3)(S + 3)

(S - 9)(S + 1) = 0
S, or speed in still water = mph OR S = - 1 (ignore)
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