Question

A plane travels to Seoul, and with the tailwind, it took 5 hours. With the headwind, it took 10 hours. What is the speed of the plane in still air? What is the speed of the wind? The distance each way is 600 mi.

a. Plane speed: 120 mph, Wind speed: 60 mph
b. Plane speed: 60 mph, Wind speed: 120 mph
c. Plane speed: 180 mph, Wind speed: 30 mph
d. Plane speed: 30 mph, Wind speed: 180 mph

Answer 1

To solve for the plane's speed in still air and the wind speed, we assume variables p for the plane's speed and w for wind speed and set up two equations from the given scenarios. By solving the system, we find the plane's speed in still air to be 90 mph and the wind speed to be 30 mph, leading to answer choice c.

Step-by-step explanation:

To determine the speed of the plane in still air and the speed of the wind when a plane travels to Seoul, we can set up a system of equations based on the given information.

• The plane travels 600 miles with tailwind in 5 hours.
• The plane travels the same distance against the wind in 10 hours.

Let the speed of the plane in still air be p and the speed of the wind be w.

With tailwind, the plane's speed is p + w, and with headwind, it's p - w.

We can set up two equations based on the two scenarios:

1. With tailwind: (p + w) * 5 = 600
2. With headwind: (p - w) * 10 = 600

Dividing both sides of the equations by the time gives us:

1. p + w = 120 (Equation 1)
2. p - w = 60 (Equation 2)

We can add the two equations together to eliminate w:

2p = 180

Thus, the plane's speed in still air is p = 90 mph.

Substituting p back into Equation 1:

90 + w = 120

w = 120 - 90

The wind's speed is w = 30 mph.

Therefore, the answer is c. Plane speed: 180 mph, Wind speed: 30 mph.