Respuesta :
So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:
[tex]\begin{gathered} 2v+40\frac{mi}{h}=\frac{1180mi}{2h}=590\frac{mi}{h} \\ 2v=590\frac{mi}{h}-40\frac{mi}{h}=550\frac{mi}{h} \\ v=\frac{550\frac{mi}{h}}{2}=275\frac{mi}{h} \end{gathered}[/tex]Then we get:
[tex]v+40\frac{mi}{h}=275\frac{mi}{h}+40\frac{mi}{h}=315\frac{mi}{h}[/tex]Then the speeds of the planes are 275mph and 315mph.
