Questions: Flying against the wind, a jet travels 1710 miles in 3 hours. Flying with the wind, the same jet travels 1820 miles in 3 hours. What is the rate of the jet in still air? Rate of the wind: Rate of the jet in still air:

Solution Steps

To find the rate of the jet in still air, we need to set up two equations based on the given information. Let \( j \) be the rate of the jet in still air and \( w \) be the rate of the wind. When flying against the wind, the effective speed of the jet is \( j - w \), and when flying with the wind, it is \( j + w \). We can use the formula for speed, which is distance divided by time, to set up the equations:

1. Against the wind: \( \frac{1710}{3} = j - w \)
2. With the wind: \( \frac{1820}{3} = j + w \)

Solve these two equations simultaneously to find the values of \( j \) and \( w \).

We start by defining the variables:

• Let \( j \) be the rate of the jet in still air.
• Let \( w \) be the rate of the wind.

From the problem, we can derive two equations based on the distances traveled against and with the wind:

1. Against the wind: \[ \frac{1710}{3} = j - w \implies 570 = j - w \]
2. With the wind: \[ \frac{1820}{3} = j + w \implies 606.6667 = j + w \]

We can solve the two equations simultaneously:

1. From the first equation, we have: \[ j = 570 + w \]

2. Substituting this expression for \( j \) into the second equation: \[ 606.6667 = (570 + w) + w \implies 606.6667 = 570 + 2w \] Rearranging gives: \[ 2w = 606.6667 - 570 \implies 2w = 36.6667 \implies w = 18.3333 \]

3. Now substituting \( w \) back into the expression for \( j \): \[ j = 570 + 18.3333 = 588.3333 \]

Final Answer