[tex]\begin{gathered} v=\text{spe}ed\text{ of the dron= 5 miles/hour} \\ v_w\text{ = wind sp}eed \\ \text{With the wind} \\ x1=21\text{ miles},\text{ v}1=v+v_w\text{ } \\ \text{againt the wind} \\ x2=9\text{ miles},\text{ v2=}v-v_w\text{ } \\ v=\frac{x}{t} \\ \text{Solving t} \\ t=\frac{x}{v} \\ \text{But the time is equal in both cases} \\ t1=t2 \\ \frac{x1}{v1}=\frac{x2}{v2} \\ \\ \frac{x1}{v+v_w\text{ }}=\frac{x2}{v-v_w\text{ }} \\ Solv\text{ing }v_w \\ x1(v-v_w)=x2(v+v_w) \\ x1v-x1v_w=x2v+x2v_w \\ x1v-x2v=x2v_w+x1v_w \\ v(x1-x2)=v_w(x2+x1) \\ v_w=\frac{v(x1-x2)}{(x2+x1)} \\ U\sin g\text{ the values} \\ v_w=\frac{(\text{5 miles/hour})(21\text{ miles}-9\text{ miles})}{(9\text{ miles}+21\text{ miles})} \\ \\ v_w=2\text{ miles/hour} \\ \text{The wind sp}eed\text{ is }2\text{ miles/hour} \end{gathered}[/tex]
