Q. 62 - Precalculus Enhanced with Graphing Utilities

Question

The average airspeed of a single- engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?

Step-by-Step Solution

Answer

Wind speed is 30 mi/hour

Step 1: Given information

we are given The average airspeed of a single- engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind 

Step 2: Write the equations and solve them

The average airspeed of a single- engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind 

Let x be wind speed and y be distance

We get

$$\begin{gathered} 2(150+x)=y \\ 300+2x=y \left(1\right) \end{gathered}$$

it flew in 3 hours against the wind 

$$\begin{gathered} 3(150-x)=y \\ 450-3x=y \end{gathered}$$                 (2)

Equate both equations

$$\begin{gathered} 300+2x=450-3x \\ 5x=150 \\ x=30 \end{gathered}$$

Step 3: Conclusion

Wind speed is 30 mi/hour