the speed of the current in a river is 6 mph a ferry operator who works that part of the river is looking to buy a new boat for his business everyday his route takes him 22.5 miles against the current and back to his deck and he needs this trip in a total of 9 hours he has a boat in mind but he can only test it on a lake where there in no current how fast must the boat go on the lake in order for it to serve the ferry operators needs?
i understand the problem i just need help writing it out. ty!
time = distance/speed
If his boat has speed s, then the time upstream + the time downstream adds up to 9 hours, so
22.5/(s-6) + 22.5/(s+6) = 9
yes, algebra is math.
thank you !!:)
is this math?
Sure! Let's break down the information given and try to write out the problem:
1. The speed of the current in the river is 6 mph.
2. The ferry operator needs to travel a round trip of 22.5 miles against the current.
3. The ferry operator wants to complete the trip in a total of 9 hours.
4. The boat can only be tested on a lake with no current.
Now, let's define the variables:
Let's call the speed of the boat on the lake "x" mph.
To solve the problem, we need to calculate the time it takes to travel against the current on the river and back.
Let's consider the time taken to travel against the current:
Distance = 22.5 miles
Speed of the boat = x mph
Speed of the current = 6 mph
The effective speed of the boat against the current would be x - 6 mph.
Using the formula: Time = Distance / Speed, we can calculate the time taken to travel against the current:
Time against the current = Distance / (x - 6)
Similarly, we can calculate the time taken to travel with the current:
The effective speed of the boat with the current would be x + 6 mph.
Time with the current = Distance / (x + 6)
Now, let's write the equation:
Time against the current + Time with the current = 9
(Distance / (x - 6)) + (Distance / (x + 6)) = 9
By solving this equation, we can find the value of x (the speed of the boat on the lake) required for the ferry operator to meet their needs.
I hope this helps you write out the problem! Let me know if you need any further assistance.