Question

1. An airplane flew 3000 miles in 5 hours against the wind and 4 hours with the wind. Find the

speed of the airplane and the speed of the wind.
Step 1: ___________________________________________________________
Step 2: What are you looking for in this problem?
___________________________________________________________
Step 3: Name what you are looking for. Choose a letter to represent the quantity.
Let _________: be the speed of __________________________
_________: be the speed of __________________________
Fill out the table.
Rate Time Distance
The formula you need to remember:_______________________________
Step 4: Translate words into algebraic expressions and equations.
Step 5: Solve the equation.
Step 6: Check the answer.
Step 7: Answer the question with a complete sentence.

Answer 1

The speed of the airplane and the speed of the wind, obtained from the formula for speed are;

Speed of the airplane = 675 mph

Speed of the wind = 75 mph

What is the formula for the speed of an object?; The speed of an object is the ratio of the distance traveled to the duration of travel of the object

Let p represent the speed of the airplane and let v represent the speed of the wind, we get;

p - w = 3000 miles/5 hours

p - w = 600 mph...(1)

p + w = 3000 miles/ 4 hours

p + w = 750 mph...(2)

Adding the left and right hand sides of equation (1) and (2), we get;

Left hand side; (p - w) + (p + w) = 2·p

Right hand side; 600 + 750 = 1350

2·p = 1,350 mph

p = 1,350/2

The speed of the airplane, p = 675 mph

p - w = 600

w = p - 600

w = 675 - 600

675 - 600 = 75

The speed of the wind, w = 75 mph