Hello, maryanna91!

Im not quite sure how to set this word problem up.

I'm not surprised, you've mixed *two* word problems. Two boats leave simultaneously from the same port.

One travels due north and the other flies due west.

The northbound boat flies 5 mph faster than the eastbound boat,

and after 2 hours the planes are 100 miles apart.

Find the rate at which each boat is traveling. I'll take a *guess* at what you meant . . . Code:

o N
* ↑
100 * ↑
* ↑ 2(x+5)
* ↑
* ↑
W o ← ← ← ← ← o P
2x

Let $\displaystyle x$ = rate of the westbound boat (in mph).

Then $\displaystyle x+5$ = rate of the northbound boat.

They start together at P.

After 2 hours, the westbound boat travels $\displaystyle 2x$ miles to $\displaystyle W.$

During the same 2 hours, the northbound boat travels $\displaystyle 2(x+5)$ miles to $\displaystyle N.$

At that time, they are 100 miles apart: .$\displaystyle NW = 100$

Pythagorus says: .$\displaystyle (2x)^2 + [2(x+5)]^2 \:=\:100^2$

. . which simplifies to: .$\displaystyle 2x^2 + 40x - 2475 \:=\:0$

Quadratic Formula: .$\displaystyle x \;=\;\frac{-10 \pm\sqrt{19,\!900}}{4}$

. . The positive root is: .$\displaystyle x \;=\;32.76683995 $

Therefore: .$\displaystyle \begin{Bmatrix}\text{westbound} &\approx& 32.8\text{ mph} \\ \text{northbound} &\approx& 37.8\text{ mph} \end{Bmatrix}$