SOLUTION: 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

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Question 1060598: 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!)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
             SPEED         TIME       DISTANCE
DOWN         r+2                        8
UPRIVER      r-2                        4
Total                       2


             SPEED         TIME       DISTANCE
DOWN         r+2           8/(r+2)      8
UPRIVER      r-2           4/(r-2)      4
Total                       2

highlight%288%2F%28r%2B2%29%2B4%2F%28r-2%29=2%29

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
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!)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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%2F%28u%2B2%29 hours.

The boat travels 4 miles  upstream  in 4%2F%28u-2%29 hours.

According to the condition,

8%2F%28u%2B2%29 = 4%2F%28u-2%29.

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%2F4 = 5.

Anser.  The boat speed in still water is 5 miles per hour.

Solved.

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

Ignore writing by "josgarithmetic".