Answer:
[tex] \frac{55x + 75 x}{1375}= 2[/tex]
[tex] 13 x = 2750[/tex]
[tex] x = \frac{2750}{13}= 211.538 mi[/tex]
and [tex] 3x = 3*211.538 = 634.614[/tex]
So then the total lenght is :
[tex] x + 3 x= 4x = 4*211.538=846.152 miles[/tex]
Step-by-step explanation:
For this case we assume that:
x (miles) represent the distance driven in town at a speed of 25 mph
3x (miles) would represent the distance for country road at a speed of 55 mph
And we know that the total time is 2hr.
Let [tex] t_1[/tex] the time for the town and [tex] t_2 [/tex] the time for the country, we can set up the following equation for the time:
[tex] t_1 + t_2 = 2[/tex]
From the definition of distance we have that D = vt if we solve for the time we got t= D/v and if we replace we got:
[tex] \frac{x}{25}+ \frac{3x}{55} =2[/tex]
And now we can solve for x like this:
[tex] \frac{55x + 75 x}{1375}= 2[/tex]
[tex] 13 x = 2750[/tex]
[tex] x = \frac{2750}{13}= 211.538 mi[/tex]
and [tex] 3x = 3*211.538 = 634.614[/tex]
So then the total lenght is :
[tex] x + 3 x= 4x = 4*211.538=846.152 miles[/tex]
