The speed of a stream is 3 mph. A boat travels 5 miles upstream in the same time it takes to travel 11 miles downstream. What is the speed of the boat in still water?
Speed up stream = x -3 (-3 because the stream movement will be negative in relation to the boat) and the boat will travel 5 miles
$\displaystyle x-3=5$
$\displaystyle x=5+3$
$\displaystyle x=8$
You can check using the other data.
Speed down stream = x+3 (because the stream and boat movement will add) and the boat will travel 11 miles
$\displaystyle x+3=11$
$\displaystyle x=11-3$
$\displaystyle x=8$
Now you see, the boat -on still water- travels at 8 mph.
Hello, magentarita!
Another approach . . .
We'll use: .$\displaystyle \text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}$
Let $\displaystyle x$ = boat's speed in still water.The speed of a stream is 3 mph.
A boat travels 5 miles upstream in the same time it takes to travel 11 miles downstream.
What is the speed of the boat in still water?
Going upstream, the current works against the boat. .The boat's speed is $\displaystyle x - 3$ mph.
. . It went $\displaystyle 5$ miles at $\displaystyle x-3$ mph. .This took: .$\displaystyle \frac{5}{x-3}$ hours.
Going downstream, the current works with the boat. .The boat's speed is $\displaystyle x+3$ mph.
. . It went $\displaystyle 11$ miles at $\displaystyle x+3$ mph. .This took: .$\displaystyle \frac{11}{x+3}$ hours.
These two times are equal: .$\displaystyle \frac{5}{x-3} \:=\:\frac{11}{x+3}\quad\hdots\quad There!$