Question 329126
The trick to these rate roblems is to read them carefully.

Note that it says, "the plane can fly 7 miles with the wind IN THE SAME AMOUNT OF TIME as it can fly 5 miles against the wind". By the statement, "in the same amount of time", it tells use we want to solve d=rt for t=d/r and set one time equal to the other.
We are asked to find the wind rate, so we know that r must appear in the equation.

It flies 5 miles against the wind in 5/(180-r) hours.

It flies 7 miles with the wind in 7/(180+r) hours.

The problem says these are equal, so we have:

{{{5/(180-r)=7/(180+r)}}}

{{{r=30}}} mph for the wind rate.