.
Julia's Boston Whaler cruised 45 miles upstream and 45 miles back in a total of 8 hours. The speed of the river is 3 mph. Find the speed of the boat in still water
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let 
be the unknown speed of the boat in still water (in miles per hour).
When the boat moves upstream, its speed relative to the bank of the river is 
miles per hour,
and the time spent moving upstream is 
hours.
When the boat moves downstream, its speed relative to the bank of the river is 
miles per hour,
and the time spent moving downstream is 
hours.
So, the total time upstream and downstream is 
, and it is equal to 8 hours, according to the problem's input.
This gives an equation 
.
To simplify the equation, multiply both sides by 
and collect like terms. Step by step, you will get
= 
,
= 
,
,
= 
.
Now cancel both sides by the factor 2. You will get
= .
Apply the quadratic formula
= 
= 
= 
.
You need only positive root u = 
= 12.
The boat speed in still water is 12 mph.
Answer. The boat speed in still water is 12 mile per hour.
