1. ## Story problem

BOAT
.|
.|2 Miles
.|______________________
.......4 miles of shoreline.....|
.....................................| 1Mile
.................................HOUSE
Art rows @ 2 MPH and walks @ 4 MPH

Art rowed to a point x miles down the shore towards his house and then walked directly to his house.

I believe I have this part correct:
Walking distance in terms of x: f(x) = sqrt of (4-x+1)
Rowing distance in terms of x: f(x) = sqrt of (x^2+4)
Time walking in terms of x: f(x) = sqrt of (4-x+1) all divided by 4
Time rowing in terms of x: f(x) = sqrt of (x^2+4) all divided by 2

Let me know if I'm OK so far.

Write a function, T(x), for the total time it takes to get to Art's house from where he is located in the boat. Wouldn't I just add the last two functions together for the function for total time?

2. Originally Posted by galanm
BOAT
.|
.|2 Miles
.|______________________
.......4 miles of shoreline.....|
.....................................| 1Mile
.................................HOUSE
Art rows @ 2 MPH and walks @ 4 MPH

Art rowed to a point x miles down the shore towards his house and then walked directly to his house.
Assuming you mean x to stand for the distance between the ending of the direct line to shore (where you have the "2 Miles" line meet the horizontal line, above) and the point where the boat actually landed, then the Pythagorean Theorem (or the Distance Formula) should give you the following "distance" expressions:

. . .boat:
. . . . .sqrt[2^2 + x^2] = sqrt[4 + x^2]

. . .land:
. . . . .sqrt[(4 - x)^2 + 1^2] = sqrt[17 - 8x + x^2]

Since d = rt, then t = d/r, so the "time" expressions will be:

. . . . .boat: (sqrt[4 + x^2])/2
. . . . .land: (sqrt[17 - 8x + x^2])/4

Add the expressions for the two partial times to get an expression for the total time.

3. I see I forgot about squaring the 4-x. Thanks.