Question 123956: Vincent's boat will go 13 miles per hour in still water. If he can go 14 miles downstream in the same amount of time as it takes to go 8 miles upstream, then what is the speed of the current?
(Please round your answer to one decimal place.)
Answer by PBMathandscience(9)   (Show Source):
You can put this solution on YOUR website! Let C be the speed of the current. When going downstream, the speed of the current is added to the speed of the boat in still water. So, when going downstream the speed over the ground is 13 + C. When going upstream, the speed of the current is subtracted from the speed of the boat in still water, so the upstream speed over the ground is 13 - C.
Distance = Speed x Time, or Time = Distance/Speed. The time it takes to go 14 miles downstream is therefore 14/(13+C). The time it takes to go 8 miles upstream is 8/(13-C). But we know the times are equal, so:
 .
Multiply both sides by (13-C):
Replace the  on the left hand side by 1, and multipy both sides by (13+C):
Simplify by replacing the  by 1 to give:
Multiply this out to give:
 or
Now, subtract 104 from both sides, and add 14C to both sides:
Again, simplify:
Divide both sides by 22 to give the answer:
Now check the answer. The speed downstream is 13+C, or 16.545. To cover 14 miles downstream takes 14/16.545 hours, or .846 hours. The speed upstream is 13-C, or 9.455. To cover 8 miles upstream takes 8/9.455 hours, or .846 hours. The times are the same, the solution works.
|
|
|
