Question

An airplane flies 1200 miles into the wind in 3 hours. The return trip takes 2 hours. Find the speed of the airplane without a wind and the speed of wind.

Answer 1

from what is given in your question, we have the following two equations:
\[\nu_{plane}-\nu_{air}={1200 miles \over 3 hours}=400mph \rightarrow(1)\]
\[v_{plane}+v_{air}={1200 miles \over 2 hours}=600mph\]
solve the two equation to find both velocities

Answer 2

adding equation (1) and (2), we get:
\[2\nu_{plane}=1000 mph \implies \nu_{plane}=500mph\]
substitute in either equation (1) by v_plane=500, you get:
\[500-\nu_{air}=400mph \implies \nu_{air}=100mph\]

Answer 3

does that make sense to you?

Answer 4

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Answer 5

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Answer 6

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Answer 7

you're welcome