Answer:
The value is [tex]t = 4 \ hours[/tex]
Step-by-step explanation:
From the question we are told that
The initial position of the car is [tex]x_i , y_i = (-5,7)[/tex]
The final position of the car is [tex]x_f , y_f = (-5,-1)[/tex]
The speed of the car is [tex]v = 40 \ miles / hour[/tex]
Generally the distance covered by the car along the x-axis is
[tex]x = -5 - [- 5][/tex]
=> [tex]x = 0[/tex]
Generally the distance covered along the y-axis is
[tex]y = y_i - y_f[/tex]
=>[tex]y = y_i - [-1][/tex]
=> [tex]y = 8[/tex]
Generally the resultant distance covered is
[tex]R = \sqrt{x^2 + y^2}[/tex]
=> [tex]R = \sqrt{0^2 + 8^2}[/tex]
=> [tex]R = 8[/tex]
From the question we are told that 1 unit of the distance covered is 20 miles so
8 units is
[tex]r = 8 *20[/tex]
=> [tex]r =160 \ miles[/tex]
Generally the time taken is mathematically represented as
[tex]t = \frac{r}{v}[/tex]
=> [tex]t = \frac{160}{ 40}[/tex]
=> [tex]t = 4 \ hours[/tex]
