SOLUTION: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the current.

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Question 1134504: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the current.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
.
Let "c" be the speed of the current, in miles per hour.


Then the speed downstream is  (16+c) miles per hour, while the speed upstream is (16-c) miles per hour.


The time traveling 15 miles downstream is   hours.

The time traveling  9 miles   upstream is   hours.


From the condition, you have this "time" equation


     =    hours.


To solve it, multiply both sides by  (16+c)*(9-c).  You will get


    15*(16-c) = 9*(16+c).


Simplify and solve:

   15*16 - 15c = 9*16 + 9c

   15*16 - 9*16 = 9c + 15c

    6*16 = 24c

    c =  =  = 4.


ANSWER.  The currecnt speed is 4 miles per hour.

Solved.

-------------------

It is a typical and standard Upstream and Downstream trip word problem.

You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site, where you will find other similar solved problems with detailed explanations.

Read them attentively and learn how to solve this type of problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems",  the topic "Travel and Distance problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


If the times are the same, then the ratio of distances is the same as the ratio of speeds.

Let c be the speed (mph) of the current. Since the boat's speed in still water is 16, the upstream and downstream speeds are 16-c and 16+c. Then, since the boat can go 15mi downstream in the same time is can go 9mi upstream,






The speed of the current is 4mph.

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