Question

if it would take billy an hour to race over to his girlfriends house and two hours if he went 20 miles per hour slower how far aways does billys girlfriend live

Answer 1

Recall your d = rt, distance = rate * time.

now, let's say she lives "d" miles away, and so if Billy goes say at "r" mph fast to her house, he gets there in 1hr.

now, if he goes 20 mph slower, namely " r - 20 " mph, he gets there in 2 hours, same "d" miles.

$\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Billy}&d&r&1\\ \textit{slower Billy}&d&r-20&2 \end{array} \\\\\\ \begin{cases} d=r(1)\implies d=\boxed{r}\\ d=2(r-20)\\ ----------\\ d=2\left( \boxed{d}-20 \right) \end{cases} \\\\\\ d=2d-40\implies 40=d$