SOLUTION: A motorboat can maintain a constant speed of 24 miles per hour relative to the water. the boat makes a trip upstream to a certain point in 35 minutes; the return trip takes 25 minu

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Question 1183951: A motorboat can maintain a constant speed of 24 miles per hour relative to the water. the boat makes a trip upstream to a certain point in 35 minutes; the return trip takes 25 minutes. what is the speed of the current?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
A motorboat can maintain a constant speed of 24 miles per hour relative to the water.
The boat makes a trip upstream to a certain point in 35 minutes; the return trip takes 25 minutes.
What is the speed of the current?
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Let "c" be the speed of current.


The effective speed traveling downstream is 24+c miles per hour;  

the distance traveling downstream is  %2825%2F60%29%2A%2824%2Bc%29  miles.


The effective speed traveling upstream is 24-c miles per hour;  

the distance traveling downstream is  %2835%2F60%29%2A%2824-c%29  miles.


So we write equation saying that the distance is the same in both directions

    %2825%2F60%29%2A%2824%2Bc%29 = %2835%2F60%29%2A%2824%2Bc%29.


Simplify and find "c"

    25*(24+c) = 35*(24-c)

    25*24 + 25c = 35*24 - 35c

    25c + 35c = 35*24 - 25*24

        60c   = 10*24 = 240

          c   = 240%2F60 = 4.


ANSWER.  The speed of the current is 4 miles per hour.

Solved.




Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor showed a good standard formal algebraic solution.

If a formal algebraic solution is not required, here is a quick way to get the answer in a few seconds mentally.

(1) The upstream speed is the speed of the boat minus the speed of the current; the downstream speed is the speed of the boat plus the speed of the current. That means the speed of the boat is halfway between the upstream and downstream speeds.

(2) The distances are the same, and the ratio of the times is 35:25 = 7:5; that means the ratio of upstream and downstream speeds is 5:7.

(1) and (2) together tell us that the ratio 5:6:7 shows the ratio of the upstream speed, the speed of the boat, and the downstream speed. And since the speed of the boat is 24mph, the upstream speed is 20mph and the downstream speed is 28mph; the speed of the current is 4mph.

That's a lot of words to explain the solution method -- but the actual mental calculations take only a very little time.