Ship A is 100 km west of ship B.

Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h.

Find the fast is the distance between the ships changing at time 4:00 PM.

At any time ,

Consider the distance traveled by the ship A as  .

Consider the vertical distance traveled by the ship B as  .

Consider the distance between the ships is .

Diagram of the situation at any time :

From the above figure,

Apply Pythagorean theorem to the above diagram.

.

Differentiate on each side with respect to .

Ship A is sailing east at 35 km/h.

Therefore,  km/h.

Ship B is sailing north at 25 km/h.

Therefore,  km/h.

Rate at which distance between two ships changing at any time  is .

Find the distance traveled by ship A in 4 hours is .

Distance = speed  time.

Find the distance traveled by ship B in 4 hours is .

Find the distance between the ships at 4.00 PM.

.

Substitute  and  in above expression.

Consider the result in (1) .

Substitute corresponding values in above expression.

Rate at which distance between two ships changing at 4:00 Pm is  km/h.

Rate at which distance between two ships changing at 4:00 Pm is  km/h.