Lest organize and label the information the problem is giving us first:
We know that the total time of the trip is 9 hours, so
. We also know that the total distance of the trip is 22.5 miles, so 
. And we also know that the speed of the current is 6 mph, so 
.
Now, lets organize and label the things we don't know:
We don't know the speed of the boat in the lake, so
. We don't know the time of the trip against the current, so 
. We don't know the time of the trip with the current, so 
The next thing we are going to do is set up equations to relate the things we don'k know with the things we actually know.
If the distance of the whole trip is 22.5 miles, the distance of the trip against the current is
, so 
. Similarly, the distance with the current is 11.25, so 
.
Now lets use the equation
to solve our problem:
Speed of the boat against the current:
equation (1)
Speed of the boat with the current:
equation (2)
Notice that we don't know the values of
and 
, but we cant take advantage of the fact that the total time of the trip is 9 hours, so 
. Lets solve this equation for :
equation (3)
Now we can replace equation (3) in equation (2) to express our equations with only tow variables:
equation (4)
Next, lets solve for in equation (4):
equation (5)
Replace equation (5) in equation (1):
equation (6)
Finally, we can solve equation (6) to find the speed of the boat in the lake:
Using the quadratic formula to solve our quadratic equation, we get that S_{l}= 7.38 or
. Since speed cannot be negative, the solution of our equation is 
.
We can conclude that the speed of the boat on the lake <span>must be 7.38 mph in order for it to serve the ferry operator’s needs.</span>
We know that the total time of the trip is 9 hours, so
Now, lets organize and label the things we don't know:
We don't know the speed of the boat in the lake, so
The next thing we are going to do is set up equations to relate the things we don'k know with the things we actually know.
If the distance of the whole trip is 22.5 miles, the distance of the trip against the current is
Now lets use the equation
Speed of the boat against the current:
Speed of the boat with the current:
Notice that we don't know the values of
Now we can replace equation (3) in equation (2) to express our equations with only tow variables:
Next, lets solve for
Replace equation (5) in equation (1):
Finally, we can solve equation (6) to find the speed of the boat in the lake:
Using the quadratic formula to solve our quadratic equation, we get that S_{l}= 7.38 or
We can conclude that the speed of the boat on the lake <span>must be 7.38 mph in order for it to serve the ferry operator’s needs.</span>