Answer
Rate of plane in still air: $180$ $mph$
Rate of wind: $20$ $mph$
Work Step by Step
A pertinent formula for this exercise is $Rate \times Time = Distance$. This means that, when taking into account the information from the exercise, we can write the following system of equations: $$4(A + W) = 800$$ $$5(A - W) = 800$$ which is to say: $$A + W = 200$$ $$A - W = 160$$where $A$ is the plane's rate in still air and $W$ is the rate of the wind. To solve the system, we can use the substitution method: $$A - W = 160$$ $$A = 160 + W$$ Therefore, $$A + W = 200$$ $$(160 + W) + W = 200$$ $$2W = 40$$ $$W = 20$$ Using this value, we "plug" it into the previous equation: $$A = 160 + W$$ $$A = 160 + (20) = 180$$
