Question

How far do kala live from the mountains

Answer 1

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

let's say the rate of speed for Kala was "r" on the way over to the mountains.

Now, on the way over, it took 8 hours due to heavy traffic, whilst on the way back it took only 5 hours since there was no traffic.

The distance covered, say "d" miles, is the same on the way over as well as on the way back.


`\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{to the mountains}&d&r&8\\ \textit{to back home}&d&r+21&5 \end{array} \\\\\\ \begin{cases} d=8r\implies (d)/(8)=\boxed{r}\\ d=5(r+21)\\ ----------\\\\ d=5\left(\boxed{(d)/(8)}+21 \right) \end{cases} \\\\\\ d=5\left( \cfrac{d+168}{8} \right)\implies d=\cfrac{5d+840}{8}\implies 8d=5d+840 \\\\\\ 3d=840\implies d=\cfrac{840}{3}\implies d=280`