Question

Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than the other car. The cars are 300 miles apart in 3h. How fast is each car traveling?

Answer 1

Recall your d = rt, distance =  rate * time

let's say we have two cars, A and B, B has a speed rate of "r", so A is the faster one and has a speed rate of " r + 10 "

they both are 300 miles apart after 3hrs, after 3hrs, car has been running for 3hrs, and car B has also been running for 3hrs, so their time is the same

we know their distances added up, is 300miles, so if car B covered say, "d" distance on those 3hrs, car A covered the slack, " 300 - d "

$\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{car A}&300-d&r+10&3\\ \textit{car B}&d&r&3 \end{array}\\\\ -------------------------------\\\\ \begin{cases} 300-d=(r+10)3\\ \boxed{d}=3r\\ ----------\\ 300-\boxed{3r}=3(r+10) \end{cases}$

solve for "r"