Question 1026141
.
The speed of a stream is 5 mph. A boat travels 9 miles upstream in the same time it takes to travel 19 miles downstream. What is the speed of the boat in still water?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let u = the speed of the boat in still water.

Then the speed of the boat relative the bank of the river is u-5 {{{km/h}}} when it moves upstream, and u+5 when it moves downstream.

We can write the basic equation for travel and distance problems 

Time = {{{Distance/Speed}}}  

in the form  

t = {{{9/(u-5)}}}    (1)  for moving upstream, and

t = {{{19/(u+5)}}}   (2)  for moving downstream.

Since the left side, t, is the same in both equations, you get a single equation for u

{{{9/(u-5)}}} = {{{19/(u+5)}}}.

To solve it, multiply both sides by the product (u-5)*(u+5) and simplify:

9*(u+5) = 19*(u-5),

9u + 45 = 19u - 95,

45 + 95 = 19u - 9u,

10u = 140,

u = {{{140/10}}} = 14 mph.

It is your answer: the speed of the boat in still water is 14 miles per hour.
</pre>