SOLUTION: when lucy swims with the current, she swims 18km in 2 hours. against the current she can swim only 14km in the same time. how fast can lucy swim in still water? what is the rate of

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: when lucy swims with the current, she swims 18km in 2 hours. against the current she can swim only 14km in the same time. how fast can lucy swim in still water? what is the rate of      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 134378: when lucy swims with the current, she swims 18km in 2 hours. against the current she can swim only 14km in the same time. how fast can lucy swim in still water? what is the rate of the current?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Using the basic formula for distance, i.e. d = r*t where d = distance travelled, r = the rate of travel (speed), and t = the time taken to cover the distance, d. We can write two equations:
d%5B1%5D+=+r%5B1%5Dt%5B1%5D for Lucy's swim with the current.
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D for Lucy's swim against the current.
We can express both r%5B1%5D and r%5B2%5D in terms of the speed of the current (C) and in terms of Lucy's swimming speed in still water (R):
r%5B1%5D+=+R%2BC Lucy's speed when swimming with the current is her speed in still water (R) plus the speed of the current (C).
r%5B2%5D+=+R-C Lucy's speed when swimming against the current is her speed in still water (R) minus the speed of the current (C).
For the first leg of the trip:
18+=+r%5B1%5D%2A2 Substitute R%2BC+=+r%5B1%5D
18+=+%28R%2BC%29%2A2 Divide both sides by 2.
9+=+R%2BC
For the second leg of the trip:
14+=+r%5B2%5D%2A2 Substitute R-C+=+r%5B2%5D
14+=+%28R-C%29%2A2 Divide both sides by 2.
7+=+R-C
So now you have two equations with two unknowns, R and C. Add these two equations to eliminate one of these variables (C):
9+=+R%2BC Add these equations.
7+=+R-C
-------------
16+=+2R Divide both sides by 2.
R+=+8Km/hr. This is Lucy's speed in still water.
Substitute this value of R into either one of the two equations we just added together:
9+=+R%2BC
9+=+8%2BC Subtract 6 from both sides.
1+=+C or C+=+1Km/hr. This is the speed of the current.