Question

Perry goes for a 4-hour trip through towns and on country roads. If she averages 65 mph on countryroads and 35 mph through towns, and if she travels three times as far on country roads as she doesthrough towns, what is the total length of her trip?

Answer 1

$364\: miles$

1) The best way to tackle this question is to think of rational equations. Since, time, rate and distance are related.

2) So, we can start writing the following:

$\begin{gathered} t=\frac{d}{r}\Rightarrow rt=d\Rightarrow t=\frac{d}{r} \\ Country\: roads=\frac{3d}{65} \\ Through\: Towns=\frac{d}{35} \end{gathered}$

So, let's solve it by equating the sum of these expressions to the spent time: 4 hours (common to both)

Now we have the LCM

$\begin{gathered} \frac{d}{35}+\frac{3d}{65}=4 \\ \frac{13d+7d}{455}=\frac{1820}{455}\times455 \\ 13d+7d=1820 \\ 20d=1820 \\ \frac{20d}{20}=\frac{1820}{20} \\ d=91 \\ 3d=273 \\ 273+91=364 \end{gathered}$

Note that adding them up, the distance in country roads and the distance in towns.