Question

In his small airplane, Steve can fly from Athens to Madrid in 9.5 hours with the wind. Against the wind, the same 1425-mile trip takes 12.5 hours. Find the speed of the plane in still air. Use two unknowns and solve the resulting system.

Option 1: Solve the system of equations for the plane's speed:

Let the speed of the plane in still air be p mph.
Let the wind speed be w mph.
With the wind, the plane's speed is (p + w) mph.
Against the wind, the plane's speed is (p - w) mph.
Using the formula: Distance = Speed x Time, we can set up the equations:
Distance = Speed x Time
1425 = (p + w) * 9.5
1425 = (p - w) * 12.5
Solve this system of equations to find the values of p and w.
Option 2: Use substitution to solve the system of equations:

Let the speed of the plane in still air be p mph.
Let the wind speed be w mph.
With the wind, the plane's speed is (p + w) mph.
Against the wind, the plane's speed is (p - w) mph.
Using the formula: Distance = Speed x Time, we can set up the equations:
1425 = (p + w) * 9.5
1425 = (p - w) * 12.5
Solve one of the equations for either p or w and substitute it into the other equation. Then, solve for the remaining variable.

Answer 1

By setting up a system of equations with the known distances and times, and solving for the variable p, we find that the plane's speed in still air is 150 mph.

Step-by-step explanation:

To determine the speed of Steve's plane in still air, we need to set up a system of equations based on the given distances and times, with p representing the plane's speed in still air and w representing the wind speed. We know the plane flies 1425 miles, which gives us two equations:

1. With the wind: 1425 = (p + w) * 9.5
2. Against the wind: 1425 = (p - w) * 12.5

We can solve the first equation for w to find w = 1425/9.5 - p, and substitute it into the second equation:

1425 = (p - (1425/9.5 - p)) * 12.5

Simplifying and solving for p, we discover the plane's speed in still air:

p = 150 mph