Respuesta :
Answer:
The whole trip took [tex]9\frac{2}{3} \ hours[/tex].
Step-by-step explanation:
For Uniform Motion in a Straight Line:
[tex]\boxed{distance\ (s)=velocity\ (v)\times time\ (t)}[/tex]
Given:
total distance (s) = 1200 km
train's velocity ([tex]v_t[/tex]) = 48 km/h
plane's velocity ([tex]v_p[/tex]) = 240 km/h
train's time ([tex]t_t[/tex]) = plane's time ([tex]t_p[/tex]) + 2 hours
Let:
train's distance ([tex]s_t[/tex]) = x km
Then:
plane's distance ([tex]s_p[/tex]) = total distance - train's distance
= (1200 - x) km
[tex]s_t=v_t\times t_t[/tex]
[tex]x=48t_t[/tex]
[tex]t_t=\frac{x}{48} \ hours[/tex] ... [1]
[tex]s_p=v_p\times t_p[/tex]
[tex]1200-x=240t_p[/tex]
[tex]t_p=\frac{1200-x}{240} \ hours[/tex] ... [2]
[tex]t_t =t_p+2[/tex]
[tex]\frac{x}{48}=\frac{1200-x}{240}+2[/tex]
[tex]\frac{5x}{240}=\frac{1200-x}{240}+2[/tex]
[tex]2=\frac{5x-(1200-x)}{240}[/tex]
[tex]2\times240=6x-1200[/tex]
[tex]6x=480+1200[/tex]
[tex]x=280\ km[/tex]
[1]
[tex]t_t=\frac{x}{48}[/tex]
[tex]=\frac{280}{48}[/tex]
[tex]=5\frac{5}{6} \ hours[/tex]
[2]
[tex]t_p=\frac{1200-x}{240}[/tex]
[tex]=\frac{1200-280}{240}[/tex]
[tex]=3\frac{5}{6} \ hours[/tex]
[tex]total\ time=t_t+t_p[/tex]
[tex]=5\frac{5}{6} +3\frac{5}{6}[/tex]
[tex]=9\frac{2}{3} \ hours[/tex]
