Q. 61 - Precalculus Enhanced with Graphing Utilities

Question

With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.

Step-by-Step Solution

Answer

The windspeed is 175mi/hour and average speed of piper is 25mi/hour

Step 1: Given information

A small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours.

Step 2: Find the equations and solve them

We get,

$$\begin{gathered} S_1=\frac{600}{3} \\ {S}_1=200mi/hr \\ And \\ {S}_2=\frac{600}{4} \\ {S}_2=150mi/hr \end{gathered}$$

now let x be the windspeed and y be the speed of the piper

A small Piper aircraft can fly 600 miles in 3 hours. 

Hence 

$x+y=200$                (1)

Also, Against this same wind, the Piper can fly the same distance in 4 hours 

$x-y=150 \left(2\right)$

Add equation 1 and 2 we get,

$$\begin{gathered} 2x=350 \\ x=175 \end{gathered}$$

Also

$$\begin{gathered} x+y=200 \\ y=200-175 \\ y=25mi/hr \end{gathered}$$

Step 3: Conclusion

The windspeed is 175mi/hour and average speed of piper is 25mi/hour