Joe flew his small airplane 900 km in 5 hours flying with the wind. He flew 700 km against the wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind... Joe flew his small airplane 900 km in 5 hours flying with the wind. He flew 700 km against the wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind. Read more

Steps to Solve

1. Identify Variables Let:

• ( x ) = speed of the airplane in still air (km/h)
• ( y ) = speed of the wind (km/h)

2. Establish Equations for With Wind When flying with the wind:

• Distance = 900 km
• Time = 5 hours

Using the formula ( \text{Speed} = \frac{\text{Distance}}{\text{Time}} ), we get: $$ x + y = \frac{900}{5} = 180 \quad \text{(1)} $$

3. Establish Equations for Against Wind When flying against the wind:

• Distance = 700 km
• Time = 7 hours

Using the same speed formula: $$ x - y = \frac{700}{7} = 100 \quad \text{(2)} $$

4. Solve the System of Equations Now we have a system of two equations:
5. ( x + y = 180 )
6. ( x - y = 100 )

Add these equations to eliminate ( y ): $$ (x + y) + (x - y) = 180 + 100 $$ This simplifies to: $$ 2x = 280 $$ Thus, $$ x = 140 \quad \text{(speed in still air)} $$

5. Find the Speed of Wind Substituting ( x = 140 ) back into equation (1): $$ 140 + y = 180 $$ Therefore, $$ y = 180 - 140 = 40 \quad \text{(speed of wind)} $$