Question 1060014
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Hi! I am the father of an exasperated 9th grader. Thank you SO MUCH for being there! Here is the question that is stumping her: 

A boat travels 35 km upstream and then back again in 4 hours 48 minutes. If the speed of the boat in still water is 15 km/hr, what is the speed of the current? 

Thank you, 
Tim in Massachusetts 
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<pre>
Let "v" be the speed of the current, in km/h.

Then the speed of the boat traveling upstream   is (15-v) km/h,
     the speed of the boat traveling downstream is (15+v) km/h.

The time traveling 35 km upstream   is {{{35/(15-v)}}} hours.
The time traveling 35 km downstream is {{{35/(15+v)}}} hours.

The total time is 4 hours 48 minutes = {{{4}}} {{{48/60}}} hour = {{{4}}} {{{4/5}}} hour = {{{24/5}}} hour, 
which gives an equation 

{{{35/(15-v) + 35/(15+v)}}} = {{{24/5}}}.

To solve it, multiply both sides by 5*(15-v)*(15+v). You will get

35*5*(15+v) + 35*5*(15-v) = 24*(225-v^2),

24v^2 = 24*225 - 2*35*5*15 = 150,

v^2 = {{{150/24}}} = {{{25/4}}},

v = {{{sqrt(25/4)}}} = {{{5/2}}} = 2.5 km/h.

<U>Answer</U>.  The speed of the current is 2.5 km/h.
</pre>

Solved.