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

`(55x + 75 x)/(1375)= 2`

`13 x = 2750`

`x = (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`

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:

`(x)/(25)+ (3x)/(55) =2`

And now we can solve for x like this:

`(55x + 75 x)/(1375)= 2`

`13 x = 2750`

`x = (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`