SOLUTION: A small motor on a fishing boat can move the boat at a rate of 14 mph in calm water. Traveling with the current, the boat can travel 48 mi in the same amount of time it takes to tr

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A small motor on a fishing boat can move the boat at a rate of 14 mph in calm water. Traveling with the current, the boat can travel 48 mi in the same amount of time it takes to tr      Log On


   

Question 1193556: A small motor on a fishing boat can move the boat at a rate of 14 mph in calm water. Traveling with the current, the boat can travel 48 mi in the same amount of time it takes to travel 36 mi against the current. Find the rate of the current.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
A small motor on a fishing boat can move the boat at a rate of 14 mph in calm water.
Traveling with the current, the boat can travel 48 mi in the same amount of time
it takes to travel 36 mi against the current. Find the rate of the current.
~~~~~~~~~~~~~~ 

Let c be the rate of current, in miles per hour.


Then effective rate with the current is 14+c mph,

while that against the current is 14-c mph.



The time traveling 36 miles against the current is  36%2F%2814-c%29  hours;

The time traveling 48 miles with    the current is  48%2F%2814%2Bc%29  hours.



The times are the same, giving you this time equation

    36%2F%2814-c%29 = 48%2F%2814%2Bc%29.



To find "c" from this equation, cross multiply


    36*(14+c)   = 48*(14-c)

    36*14 + 36c = 48*14 -48c

    48c + 36c   = 48*14 - 36*14

       84c      =    168

         c      =    168/84 = 2.


ANSWER.  The rate of the current is 2 miles per hour.

Solved.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a different method for solving this kind of problem that I personally find easier than the traditional method shown by the other tutor.

If c is the speed of the current, then the downstream speed is 14+c and the upstream speed is 14-c.

Since the times are the same, the ratio of speeds is the same as the ratio of distances:

%2814%2Bc%29%2F%2814-c%29=48%2F36=4%2F3
3%2814%2Bc%29=4%2814-c%29
42%2B3c=56-4c
7c=14
c=2

ANSWER: the speed of the current is 2 mph