At noon, ship a is 60 km west of ship b. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4: 00 pm?

The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.

Therefore, from the below triangle, we have

Let the distance between the ships is y. On applying Pythagorous theorem, we have

On substituting the value of y as

Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have

On substituting the value in above, we get

Therefore,  the distance between the ships changing at a rate of 16 km/hr at 4:00 pm

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