Question

Harry drove for 5 hours on the freeway, then decreased his speed by 20 miles per hour and drove for 6 more hours on a country road. If his total trip was 518 miles, then what was his speed on the freeway

Answer 1

so hmm recall your d = rt, or distance = rate * time

so, Harry drove 5hrs, at say a speed rate of "r", then he slowed down by 20mph, so, if he was driving at "r" mph firstly, then after he slowed down, he's driving at " r - 20"

now, we know, the total trip on the freeway and country road was 518 miles, so, if on the freeway he covered say hmmm "d" distance, on the country road he covered the slack, or 518 - d

thus   $\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{freeway}&d&r&5\\ \textit{country road}&518-d&r-20&6 \end{array}\\\\ -----------------------------\\\\ \begin{cases} \boxed{d}=5r\\ 518-d=6(r-20)\\ ----------\\ 518-\boxed{5r}=6(r-20) \end{cases}$

solve for "r"