Answer:
≈ 29 km/h
Step-by-step explanation:
If t is the number of hours since noon, then the distance between ship A and the origin is 180 − 40t, and the distance between ship B and the origin is 35t.
Using Pythagorean theorem, the distance between the ships is:
d² = (35t)² + (180 − 40t)²
d² = 1225t² + 32400 − 14400t + 1600t²
d² = 2825t² − 14400t + 32400
Taking derivative with respect to time:
2d dd/dt = 5650t − 14400
dd/dt = (2825t − 7200) / d
First, find d when t = 4.
d² = 2825 (4)² − 14400 (4) + 32400
d² = 20000
d = 100√2
Now find dd/dt.
dd/dt = (2825(4) − 7200) / (100√2)
dd/dt = 41/√2
dd/dt ≈ 29 km/h
