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?