SOLUTION: A barge movers 12 miles downstream and 8 miles upstream in a total time of 2 hours. The current in the river is 2 mph. How fast does the barge move in still water?

Question 979179: A barge movers 12 miles downstream and 8 miles upstream in a total
time of 2 hours. The current in the river is 2 mph. How fast does the barge
move in still water?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Saying that all with variables:
A barge movers D miles downstream and d miles upstream in a total
time of h hours. The current in the river is k mph. How fast does the barge
move in still water (let this unknown rate be r) ?

____________________rate___________time___________distance
DOWN________________r+k____________(____)_________D
UPST________________r-k___________(_____)_________d
Total______________________________T

Use the uniform rates travel rule to fill the missing time cells in the table
according to .

____________________rate___________time___________distance
DOWN________________r+k____________D/(r+k)_________D
UPST________________r-k____________d/(r-k)_________d
Total_______________________________T

Resulting equation is . This has the single UNKNOWN variable, r. Solve the equation for r.

-

Once that is accomplished, you have the variables assigned as
.
-
Substitute those and evaluate r.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

A barge movers 12 miles downstream and 8 miles upstream in a total
time of 2 hours. The current in the river is 2 mph. How fast does the barge
move in still water?

Let barge's speed, in still water, be S
Time taken to journey downstream, with current:
Time taken to journey upstream, against current:
Since total time taken was 2 hours, we get:
12(S - 2) + 8(S + 2) = 2(S + 2)(S - 2) ----- Multiplying by LCD, (S + 2)(S - 2)

2S(S - 10) = 0
S - 10 = 0 OR 2S = 0 (ignore)
S, or speed of barge, in still water = mph
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