Question

A military drone can fly at 5 miles per hour in calm conditions. For one flight, the drone flew 21 miles with the wind and 9 miles against the wind in the same amount of time. What was the wind speed for the flight? (Do not include the units in your response.)

Answer 1

`\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=(x)/(t) \\ \text{Solving t} \\ t=(x)/(v) \\ \text{But the time is equal in both cases} \\ t1=t2 \\ (x1)/(v1)=(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=(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}`