Question

Perry goes for a 2​-hour trip through towns and on country roads. If she averages 55 mph on country roads and 25 mph through​ towns, and if she travels three times as far on country roads as she does through​ towns, what is the total length of her​ trip?

Answer 1

Answer:

$\frac{55x + 75 x}{1375}= 2$

$13 x = 2750$

$x = \frac{2750}{13}= 211.538 mi$

and $3x = 3*211.538 = 634.614$

So then the total lenght is :

$x + 3 x= 4x = 4*211.538=846.152 miles$

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 $t_1$ the time for the town and $t_2$ the time for the country, we can set up the following equation for the time:

$t_1 + t_2 = 2$

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:

$\frac{x}{25}+ \frac{3x}{55} =2$

And now we can solve for x like this:

$\frac{55x + 75 x}{1375}= 2$

$13 x = 2750$

$x = \frac{2750}{13}= 211.538 mi$

and $3x = 3*211.538 = 634.614$

So then the total lenght is :

$x + 3 x= 4x = 4*211.538=846.152 miles$