Question

A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. What is the speed of the boat in still water? What is the speed of the current?

Answer 1

Just subtract 252 miles from 12 and 84 from 12 and add those to up

Answer 2

Same as the previous one, and again, we'll use "b" for the boat's speed in still water and "c" for the current's rate.

$\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&252&b+c&12\\ Upstream&252&b-c&84 \end{array} \\\\\\ \begin{cases} 252=12(b+c)\implies \frac{252}{12}=b+c\\ 21=b+c\implies 21-b=\boxed{c}\\ -------------\\ 252=84(b-c)\implies \frac{252}{84}=b-c\\ 3=b-c\\ ----------\\ 3=b-\left( \boxed{21-b} \right) \end{cases} \\\\\\ 3=2b-21\implies 21+3=2b\implies \cfrac{24}{2}=b$

what's the speed of the current?  well, 21 - b = c.