Question

At noon, ship A is 50km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 15km/h. How fast is the distance between the ships changing at 4:00pm.

Answer 1

the question will use similar triangles, the triangles are similar by angle angle test or postulate. So the scaling factor is 2 small triangle to large triangle, found by comparing the distance travelled in 4 hrs



you know 3a = 50 km

so a = 50/3

and using pythagoras you can find c

\[c^2 = 60^2 + (\frac{50}{3})^2\]

the distance between the 2 ships is 3c

so hopefully this helps you find the answer.