Question

Ship A is heading east toward a port at 20 mi/h and another ship B is heading north from the port at 25 mi/h. How fast is the distance S between two ships changing at the time when ship A is 30 miles away from the port and ship B is 40 miles from the port? (Don’t forget to include units in your answer.)

Answer 1

Given data is represented in figure

From figure

At x=30 , y=40

s^2= 900+1600

S^2=2500

=> s=50

differentiate wrt t

At x=30, y=40 s=50

Therefore distance between two ships is changing at a rate of 32 mi/hr