SOLUTION: A motorboat can maintain a constant speed of 34 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 35 ​minutes; the return trip takes 33

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Question 1200510: A motorboat can maintain a constant speed of 34 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 35 ​minutes; the return trip takes 33 minutes. What is the speed of the​ current?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
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c, the speed of the current

system%2834-c=d%2F%2835%2F60%29%2C34%2Bc=d%2F%2833%2F60%29%29

%2835%2F60%29%2834-c%29=%2833%2F60%29%2834%2Bc%29

35%2834-c%29=33%2834%2Bc%29
.
.

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
A motorboat can maintain a constant speed of 34 miles per hour relative to the water.
The boat makes a trip upstream to a certain point in 35 ​minutes;
the return trip takes 33 minutes. What is the speed of the​ current?
~~~~~~~~~~~~~~~~~ 

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


Then the rate of the boat moving upstream   is (34-c) miles per hour;

     the rate of the boat moving downstream is (34+c) miles per hour.


The distance of both trips is the same, so we write the distance equation

    %2834-c%29%2A%2835%2F60%29 = %2834%2Bc%29%2A%2833%2F60%29.


Multiply both sides by 60 and simplify

    (34-c)*35     = (34+c)*33

    34*35 - 35c   = 34*33 + 33c

    34*35 - 34*33 = 33c + 35c

      34*(35-33)  =    68c

         34*2     =    68c

           c      =    %2834%2A2%29%2F68 = 68%2F68 = 1.


ANSWER.  The speed of the current is 1 mile per hour.

Solved.



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


The two responses you have received until now both show a rather standard formal algebraic method for solving the problem.

Here is an alternative method that can be useful if the given information is in this particular form.

The distances are the same, and the ratio of the upstream and downstream times is 35:33, so the ratio of the upstream and downstream speeds is 33:35.

If the speed of the current is c, then the upstream and downstream speeds are 34-c and 34+c, so we have the proportion

%2834-c%29%2F%2834%2Bc%29=33%2F35

That can be solved by inspection -- the speed of the current is c = 1.

ANSWER: The speed of the current is 1 mph