Question

An airplane flying with the wind takes 2 hours to travel a distance of 360 miles. The return trip takes 3 hours flying against the wind. What is the speed of the airplane in still air and how fast is the wind blowing?

Answer:
The speed of the airplane in still air is miles per hour.
The wind speed is miles per hour.
Round your values to the nearest whole number.

Answer 1

To find the speed of the airplane in still air and the wind speed, we set up equations using the given distances and times for trips with and against the wind. Solving these equations, the airplane's speed in still air is found to be 150 mph, and the wind speed is 30 mph.

Step-by-step explanation:

To solve this problem, we establish two equations based on the given data. Let plane speed in still air be p (mph) and wind speed be w (mph).

For the trip with the wind:

• Speed with wind = p + w
• Distance = 360 miles
• Time = 2 hours
• So, 360 = (p + w) * 2

For the trip against the wind:

• Speed against wind = p - w
• Distance = 360 miles
• Time = 3 hours
• Thus, 360 = (p - w) * 3

Solving these two equations:

1. 360 = 2p + 2w
2. 360 = 3p - 3w

Divide the first equation by 2, and the second equation by 3 to simplify:

1. 180 = p + w
2. 120 = p - w

Add the two simplified equations:

180 + 120 = p + w + p - w

300 = 2p

p = 150 mph (plane speed in still air)

Substitute the value of p in one of the simplified equations to find w:

180 - 150 = w

w = 30 mph (wind speed)

Therefore, the speed of the airplane in still air is 150 miles per hour, and the wind speed is 30 miles per hour.