The speed of the current in a river is 6mph. a ferry operator who works that part of the river is looking to buy a new boat for her business. every day, her route takes her 22.5 miles each way against the current and back to her dock, and she needs to make the trip in a total of 9 hours. she has a boat in mind, but she can only test it on a lake where there is no current at all. how fast must the boat go on the lake in order for it to serve the ferry operator's needs?

The boat must be as fast as in the lake where there is no current.

Explanation:

Let the maximum speed of the boat in the lake with no current be .

The boat travels miles against the current and the other

For a boat that travels at the speed of in time , then the distance covered by the boat is calculated as below.

The speed of the current is mph.

When the boat is travelling with the current, the speed of the current will get added to the speed of the boat and the net speed of the boat becomes .

Similarly, when the boat is travelling against the current, the speed of the boat will be the difference between the speed of the boat and the speed of the current, which is .

Thus, travelling with the current, the speed of the boat is and travelling against the current will be .

The total time taken by the boat to cover the whole distance is calculated as shown below.

As the total time for the trip is hrs then substitute

Now, solve the quadratic equation to obtain the value of .

The speed cannot be a negative value therefore, the value is neglected.

Therefore, the boat must go as fast as  in no current lake to serve the ferry operators needs.

Learn More:

1. Learn more about algebraic expression

2. Learn more about lines and curves

3. Learn more about simple interest

Answer Details:

Grade: Middle School

Subject: Mathematics

Chapter: Speed, time and distance

Keywords: boat, river, current, speed, dock, maximum speed, ferry operator, distance travelled, upstream, downstream, time taken, total time.