an aircraft travels with the wind for 120 miles in 0.75 of an hour. the return trip is flown against the…

an aircraft travels with the wind for 120 miles in 0.75 of an hour. the return trip is flown against the wind and takes exactly 1 hour. which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? recall the formula d = rt. 0.75(x + y) = 120 x - y = 120 0.75(x - y)= 120 x + y = 120 120(x + y) = 0.75 120(x - y) = 1 120(x - y) = 0.75 120(x + y) = 1

an aircraft travels with the wind for 120 miles in 0.75 of an hour. the return trip is flown against the wind and takes exactly 1 hour. which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? recall the formula d = rt. 0.75(x + y) = 120 x - y = 120 0.75(x - y)= 120 x + y = 120 120(x + y) = 0.75 120(x - y) = 1 120(x - y) = 0.75 120(x + y) = 1

Answer

Explanation:

Step1: Analyze speed - with - wind

When the aircraft travels with the wind, its effective speed is the sum of the speed of the plane ($x$) and the speed of the wind ($y$), i.e., $x + y$. Given $d = 120$ miles and $t=0.75$ hours. Using the formula $d = rt$, we get $120=0.75(x + y)$.

Step2: Analyze speed - against - wind

When the aircraft travels against the wind, its effective speed is the difference between the speed of the plane ($x$) and the speed of the wind ($y$), i.e., $x - y$. Given $d = 120$ miles and $t = 1$ hour. Using the formula $d=rt$, we get $120 = 1\times(x - y)$ or $x - y=120$.

Answer:

$0.75(x + y)=120$ $x - y = 120$