# related rates help!!!

• November 15th 2007, 04:53 PM
singh1030
related rates help!!!
At noon, ship A is 125 km east of ship B. Ship A is sailing west at 35 http://maple-ta.nss.udel.edu:8080/tm...pogppajdcb.gif, and ship B is sailing north at 35 http://maple-ta.nss.udel.edu:8080/tm...pogppajdcb.gif. How fast is the distance between the ships changing at 2:00 P.M. in http://maple-ta.nss.udel.edu:8080/tm...pogppajdcb.gif?
• November 15th 2007, 05:35 PM
Soroban
Hello, singh!

Quote:

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 $t$ hours, it has moved 35t km to point A.
Then: $AP \:=\:x$, and $QA \:=\:125-35t$

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

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

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

Can you finish the problem?

• November 15th 2007, 05:39 PM
poofighter

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
• November 15th 2007, 05:50 PM
singh1030
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??