Question 1060598
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Write and solve an equation: in two hours, a motorboat can travel 8 miles down a river and return 4 miles back. 
If the river flows at 2 miles per hour, how fast can the boat travel in still water?

(If possible, can you show a step by step solution? I have a final coming up soon and this is a study guide question!)
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<pre>
Let "u" be the boat speed in still water.

Then  the boat speed traveling downstream is u+2 mph,
while the boat speed traveling  upstream  is u-2 mph.

The boat travels 8 miles downstream in {{{8/(u+2)}}} hours.

The boat travels 4 miles  upstream  in {{{4/(u-2)}}} hours.

According to the condition,

{{{8/(u+2)}}} = {{{4/(u-2)}}}.

To solve it, multiply both sides by (u+2)*(u-2). You will get

8(u-2) = 4(u+2).

Simplify and solve:

8u - 16 = 4u + 8,

8u - 4u = 8 + 16,

4u = 20   --->  u = {{{20/4}}} = 5.

<U>Anser</U>.  The boat speed in still water is 5 miles per hour.
</pre>

Solved.


It is standard, canonical and commonly used way to solve the problem and to represent/to explain the solution.


Ignore writing by "josgarithmetic".