Question 1208941
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A motorboat maintained a constant speed of 15 miles per hour relative to the water 
{{{highlight(cross(in))}}} <U>is</U> going 10 miles upstream and then returning. 
The total time for the trip was 1.5 hours. Find the speed of the current.
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<pre>
Let x be the speed of the current, in miles per hour.

The motorboat' speed with the current is 15+x mph,

and against the current is 15-x mph.


Write and use the time equation

    {{{10/(15-x)}}} + {{{10/(15+x)}}} = 1.5 hours    (1)

for the total trip.


To solve, multiply both sides by (15-x)*(15+x) = 225 - x^2.  You will get

    10(15+x) + 10*(15-x) =  1.5*(225-x^2),

    300 = 1.5*225 - 1.5*x^2,

    600 = 3*225 - 3x^2,

    3x^2 = 675 - 600,  3x^2 = 75,   x^2 = 75/3 = 25,  

    x = {{{sqrt(25)}}} = 5 mph.


<U>CHECK</U>  equation  (1):   {{{10/(15-5) + 10/(15+5)}}} = {{{10/10 + 10/20}}} = 1{{{1/2}}} hours = 1.5 hours.


<U>ANSWER</U>.  The current speed is 5 miles per hour.
</pre>

Solved.