Question

A kayaker travels xx miles per hour downstream for 3 hours. On the 4-hour return trip, the kayaker travels 1 mile per hour slower. How far did the kayaker travel in total?

Answer 1

recall your d = rt, distance = rate * time.
so, let's say hmmm not using xx, let's say his speed going downstream is "r".
Now, notice, going downstream and coming back, is the same distance, say "d" miles.
the travel downstream took 3 hours the one upstream took 4 hours.


`\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&d&r&3\\ Upstream&d&r-1&4 \end{array} \\\\\\ \begin{cases} d=3r\implies (d)/(3)=r\\ d=4(r-1)\\ --------\\ d=4\left(\boxed{(d)/(3)}-1 \right) \end{cases} \\\\\\ d=\cfrac{4d}{3}-4\implies d=\cfrac{4d-12}{3}\implies 3d=4d-12\implies 12=4d-3d \\\\\\ 12=d`

now, the kayaker went forth and back, so, the distance is d + d.