## jaydemarie4 2 years ago 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. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make 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 is no current. How fast must the boat go on the lake in order for it to serve the ferry operator’s needs?

1. omgitsmona

i can help...

2. RyanL.

Wait if this is a round trip then why does it matter what the current is. The delay in time from the current working against him will benefit him on his way back and cancel it.

3. jaydemarie4

so how do i figure it out?

4. omgitsmona

"Every day, his route takes him 22.5 miles against the current and back to his dock" -- when I first read that, it did not suggest a round trip to me. Based on that:

5. omgitsmona

rate x time = distance rate = x-6 time=9 hours distance = 22.5 9(x-6)=22.5

6. lacypennelll

*bro hoof* :D

7. omgitsmona

If you are talking about a round trip, then speed in one direction is x+6 and speed in the other direction is x-6. Since you are going the same distance in each case, your average speed is just x. So the average speed is covering 45 miles in 9 hours is 5 miles per hour with no current.

8. omgitsmona

got it? @jaydemarie4

9. hartnn

actually the equation is 22.5/(x+6) + 22.5/(x-6) = 9 let me know if you still need to know how...

10. RoseDryer

@hartnn please explain, I'm really lost.