Expert: Ahmed Salami - 12/14/2008

Question
A boat travels 10 mph in still water. It travels 24 miles upstream and the same distance downstream.  The total time it takes is 5 hours.  What is the speed of the current?

Answer
Hi Crystal,
When traveling upstream the effective speed is less because of the speed of the current. It is more when traveling downstream.
Let S(u) and S(d) be the effective speeds when traveling upstream and downstream respectively and S(c) be the speed of the current.
S(u) = 10 - S(c)
S(d) = 10 + S(c)
The time it takes to travel upstream is
24/S(u) = 24/[10 - S(c)]
Traveling downstream,
24/S(d) = 24/[10 + S(c)]
But the total time is 5 hours, so
24/[10 - S(c)] + 24/[10 + S(c)] = 5
1/[10 - S(c)] + 1/[10 + S(c)] = 5/24
{[10 + S(c)] + [10 - S(c)]}/[10 - S(c)].[10 + S(c)] = 5/24
20/[100 - S(c)^2] = 5/24
20.24 = [100 - S(c)^2].5
96 = 100 - S(c)^2
S(c)^2 = 4
S(c) = 2mph

Regards