Can someone please help me with a rational equation word problem?

Time = Distance / Speed

Let x = speed of boat in still water
Then downstream speed = x+5
upstream speed = x-5

So equating the times upstream & downstream yields:
20 / (x+5) = 10 / (x-5)

Now “cross-multiply”, i.e., multiply both sides of the equation by (x+5)*(x-5) to give:
20x – 100 = 10x + 50
etc.
Answer is 15.
This kind of problem can be tricky!
Hope that helps.

I had it that way before. My biggest problem was the set up. I got x-5 and 5-x mixed up. Thanks!!!

Well you can look at it this way:
The speed of the river current works either against or with the boat depending upon direction
Downstream speed = speed + current (adding because current helps the boat)
Upstream speed = speed – current (subtracting because the current slows the boat)
You only need to solve one of these, so lets pick downstream
20 = s + 5
s = 15

Wait a minute, @PhiNotPi—I don’t think it’s so simple. You can’t equate distance with speed. As it happens, distance figures were given for exactly one hour of travel, which need not be the case. The problem could just as easily have been stated, “The boat travels 14 miles downstream in the same time it takes it to travel 7 miles upstream.”, giving the same answer of 15 mph but with a different equation. Likewise if the river flows only 3 mph rather than 5, the same boat will travel 3 miles downstream in the time it takes to go 2 miles upstream. Still 15 mph.

@gasman you’re right. Here is my revised solution.
From the problem, you end up with a system of equations
(x+5)*t=20, and
(-x+5)*t=-10, where x is speed and t is time in hours.
The first equation simplifies to
xt+5t=20
And the second equation simplifies to
-xt+5t = -10
Add them together to make
10t=10, or
t=1
Then subtitute this into one of the first two equations
(x+5)*1 = 20
x+5=20
x=15