Chapter 3.5, Problem 18E

Reminder Round all answers to two decimal places unless otherwise indicated.

Airspeed The airspeed of a plane is its speed in the absence of wind. With a headwind, ground speed (the actual speed in relation to the ground) is decreased by the speed of the wind. With a tailwind, ground speed is increased by the speed of the wind. Let $A$ denote the airspeed of a plane and $W$ the speed of the wind, both in miles per hour. Suppose it takes the plane 9 hours to travel the 720 miles from one town to another facing a headwind of $W$. the return trip, now with a tailwind of $W$, takes only 6 hours.

a. Express the ground speed on the trip out in terms of $A$ and $W$.

b. Use the information from part a and the fact that distance equals rate times time to find an equation involving $A$ and $W$ for the trip out.

c. Express the ground speed on the return trip in terms of $A$ and $W$.

d. Use the information from part c and the fact that distance equals rate times time to find an equation involving $A$ and $W$ for the return trip.

e. Find the airspeed and the speed of the wind.