1. ## related rates help!!!

At noon, ship A is 125 km east of ship B. Ship A is sailing west at 35 , and ship B is sailing north at 35 . How fast is the distance between the ships changing at 2:00 P.M. in ?

2. Hello, singh!

At noon, ship A is 125 km east of ship B.
Ship A is sailing west at 35 km/hr, and ship B is sailing north at 35 km/hr.
How fast is the distance between the ships changing at 2:00 P.M.?

I hope you made a sketch . . .
Code:
    B *
| \
|   \
|     \
35t |       \  x
|         \
|           \
|             \
* - - - - - - - * - - - - - - *
Q    125-35t    A     35t     P
: - - - - - - 125 - - - - - - :

At noon, ship A is at point P.
In $\displaystyle t$ hours, it has moved 35t km to point A.
Then: $\displaystyle AP \:=\:x$, and $\displaystyle QA \:=\:125-35t$

At noon, ship B is at point Q.
In $\displaystyle t$ hours, it has moved 35t km to point B.

Their distance is: .$\displaystyle x \;=\;\sqrt{(125-35t)^2 + (35t)^2}$

So we have: .$\displaystyle x \;=\;\left(2450t^2 - 8750t + 15,625)^{\frac{1}{2}}$

Can you finish the problem?

d=r(t)
distance= rate(km/hr) X time from noon to 2pm is 2 hrs
70km= 35km/hr x 2 hrs

the distance is the hypothnuse of the open triangle below. use pythrugrams therom to solve for it. a^2+b^2=c^2

. l
. l70km
. l
---70km--A--125km---B
195km

4. thanks...that helps a lot. but one question. does the part about the rate of change of distance at 2 PM have no relavence to the problem? does it matter whether they ask how fast is the distance changing at 2 PM, 3 PM, 4PM and so on??