Respuesta :
Answer:
[tex] V_p = 39.9 mph[/tex]
[tex] V_c = 2(39.9) -57=22.8 mph[/tex]
Step-by-step explanation:
Notation and info given
Let's define some notation first:
[tex] V_p[/tex] represent the speed for the Private's jet
[tex] V_c[/tex] represent the speed for the Commercial jet
[tex] x[/tex] represent the total distance traveled (variable of interest)
[tex] t_c = 7 hours[/tex] represent the time to travel a distance x for the commercial jet
[tex] t_p = 4 hours[/tex] represent the time to travel a distance x for the private's jet
Solution to the problem
Since both jets are travelling the same distance we can set up the following equation:
[tex] x_c = x_p [/tex]
Form the definition of distance we know that [tex] D = v t[/tex] and if we replace this we got this:
[tex] V_c t_c = V_p t_p [/tex]
[tex] V_c (7 hours) = V_p (4 hours) [/tex]
We know that also: "If the speed of the commercial jet was 57 mph less than 2 times the speed of the private jet", so then we have this expresion:
[tex] V_c = 2 V_p -57[/tex]
And if we replace this condition we got this:
[tex] (2V_p -57) (7 hours) = V_p (4 hours) [/tex]
And we can find [tex] V_p[/tex] solving the equation like this:
[tex] 14 V_p - 399 = 4V_p[/tex]
[tex] 10 V_p = 399[/tex]
[tex] V_p = 39.9 mph[/tex]
And now we can replace in order to find [tex] v_c[/tex] like this:
[tex] V_c = 2(39.9) -57=22.8 mph[/tex]
