SOLUTION: My motor boat normally travels at 24 km/h in still water. One day I travelled 36 km against a constant current in a river and it took me the same time to travel 48 km with the curr

Algebra ->  Equations -> SOLUTION: My motor boat normally travels at 24 km/h in still water. One day I travelled 36 km against a constant current in a river and it took me the same time to travel 48 km with the curr      Log On


   

Question 207886: My motor boat normally travels at 24 km/h in still water. One day I travelled 36 km against a constant current in a river and it took me the same time to travel 48 km with the current. How fast was the current?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The basic formula is d=rt, and since the equation is based upon the fact that time up stream is equal to time downstream, it will be helpful to solve for t.
t=d%2Fr
Let x = rate of current.
24 = rate in still water

24+x = rate downstream
24-x = rate upstream

time downstream = d%2Fr=48%2F%2824%2Bx%29
time upstream = d%2Fr=36%2F%2824-x%29

Solve the equation: 48%2F%2824%2Bx%29+=+36%2F%2824-x%29+

Since a%2Fb=c%2Fd means that ad=bc,
48%2F%2824%2Bx%29+=+36%2F%2824-x%29+ means that 48%2824-x%29+=+36%2824%2Bx%29+

Get out your calculator:
1156+-48x+=+864%2B36x
1152-864+=+48x+%2B36x
288=84x
x=288%2F84=24%2F7+ km/h

R^2

Dr. Robert J. Rapalje
Altamonte Springs Campus
Seminole State University