a pilot flew a 400 - mile flight in 2.5 hours flying into the wind. flying the same rate and with the same…

a pilot flew a 400 - mile flight in 2.5 hours flying into the wind. flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind. what was the speed of the wind? 20 40 160 180

Answer

Explanation:

Step1: Calculate speed against wind

The speed of the plane against the wind is the distance divided by time. The distance $d = 400$ miles and time $t_1=2.5$ hours. So the speed against the wind $v_1=\frac{d}{t_1}=\frac{400}{2.5}=160$ miles - per - hour.

Step2: Calculate speed with wind

The speed of the plane with the wind is the distance divided by time. The distance $d = 400$ miles and time $t_2 = 2$ hours. So the speed with the wind $v_2=\frac{d}{t_2}=\frac{400}{2}=200$ miles - per - hour.

Step3: Set up equations

Let the speed of the plane in still - air be $p$ and the speed of the wind be $w$. We have the system of equations: $p - w=v_1$ and $p + w=v_2$.

Step4: Solve for wind speed

Subtract the first equation from the second equation: $(p + w)-(p - w)=v_2 - v_1$. Expanding gives $p + w - p+w=v_2 - v_1$, which simplifies to $2w=v_2 - v_1$. Substitute $v_1 = 160$ and $v_2 = 200$ into the equation: $2w=200 - 160$. $2w = 40$, then $w = 20$ miles - per - hour.