Question

A jet travels 1743mi against the wind in 3 hours and 2103mi with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the wind?

Answer 1

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

bear in mind that, say if the still air speed of the plane is say "p", and the wind has a speed of say "w", when the plane is going with the wind is not really going at "p" mph, is going at "p + w" mph.

likewise, when the plane is going against the wind, is not going "p" mph either, is really going "p - w", because the wind is eroding speed from it.


`\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{against the wind}&1743&p-w&3\\ \textit{with wind}&2103&p+2&3 \end{array} \\\\\\ \begin{cases} 1743=3(p-w)\\ (1743)/(3)=p-w\\ 581=p-w\\ \boxed{w}=p-581\\ --------\\ 2103=3(p+w)\\ (2103)/(3)=p+w\\ 701=p+w \end{cases} \\\\\\ 701=p+\left( \boxed{p-581} \right)\implies 701+581=p+p \\\\\\ 1282=2p\implies \cfrac{1282}{2}=p\implies 641=p`

so, what's the speed of the wind anyway? well, w = p - 581.