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?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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 %28rate%29%28time%29=distance.

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


Resulting equation is D%2F%28r%2Bk%29%2Bd%2F%28r-k%29=T. This has the single UNKNOWN variable, r. Solve the equation for r.

-

Once that is accomplished, you have the variables assigned as
system%28D=12%2Cd=8%2CT=2%2Ck=2%29.
-
Substitute those and evaluate r.

Answer by MathTherapy(10552) About Me  (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: 12%2F%28S+%2B+2%29 

Time taken to journey upstream, against current: 8%2F%28S+-+2%29

Since total time taken was 2 hours, we get: 12%2F%28S+%2B+2%29+%2B+8%2F%28S+-+2%29+=+2

12(S - 2) + 8(S + 2) = 2(S + 2)(S - 2) ----- Multiplying by LCD, (S + 2)(S - 2)

12S+-+24+%2B+8S+%2B+16+=+2%28S%5E2+-+4%29

20S+-+8+=+2S%5E2+-+8

2S%5E2+-+20S+-+8+%2B+8+=+0

2S%5E2+-+20S+=+0

2S(S - 10) = 0

S - 10 = 0						OR					    2S = 0 (ignore)

S, or speed of barge, in still water = highlight_green%2810%29 mph