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To determine the maximum speed the plane can travel due west, we need to consider the effect of the northwest wind.
When an airplane is flying against the wind, the wind slows it down. In this case, the northwest wind is blowing towards the southeast direction, which is opposite to the westward direction the plane wants to travel.
To find the effective speed of the plane when flying against the wind, we subtract the wind speed from the plane's maximum speed. So, to calculate the effective speed, we subtract 50 km/h (the northwest wind speed) from 200 km/h (the plane's maximum speed):
Effective speed = Max speed - Wind speed
= 200 km/h - 50 km/h
= 150 km/h
Therefore, the maximum speed the plane can travel due west, taking into account the northwest wind, is 150 km/h.