Problem 9 - Intermediate Algebra

Question

The B737-400 aircraft flies an average speed of 400 miles per hour. The expression 400 t gives the distance traveled by the aircraft in \(t\) hours Find the distance traveled by the \(\mathrm{B} 737-400\) in 5 hours.

Step-by-Step Solution

Answer

The B737-400 travels 2000 miles in 5 hours.

Step 1: Identify Given Information

The given average speed of the B737-400 aircraft is 400 miles per hour, and the time is 5 hours. We need to find out how far the aircraft will travel in 5 hours.

Step 2: Use the Expression for Distance

We use the expression \(400t\) to represent the distance traveled by the aircraft, where \(t\) is the time in hours. Substitute 5 for \(t\) in the expression.

Step 3: Substitute Time into the Expression

Replace \(t\) with 5 in the expression \(400t\), giving us \(400 \times 5\).

Step 4: Calculate the Distance

Perform the multiplication to calculate the distance: \(400 \times 5 = 2000\).

Step 5: State the Result

The distance traveled by the B737-400 in 5 hours is 2000 miles.

Key Concepts

Speed and Time

Speed and time are the key elements needed to calculate distance. When you know how fast something is going (its speed) and how long it has been traveling (its time), you can easily find out how far it has traveled.
Speed is usually measured in miles per hour (mph) or kilometers per hour (kph). Time is typically measured in hours, minutes, or seconds. In our scenario, the B737-400 aircraft has a speed of 400 miles per hour. The time of travel is given as 5 hours.
To find out how far the B737-400 travels, we multiply the speed (400 mph) by the time (5 hours). Thus, the formula for distance is:

• Distance = Speed × Time

By multiplying these numbers, you can determine that the airplane travels 2000 miles in 5 hours.

Algebraic Expressions

Algebraic expressions represent numbers and variables, often using letters to signify numbers. They can perform mathematical functions like addition, subtraction, multiplication, and division. In our example, the algebraic expression is given by:

• Expression = 400t

In this expression, the number 400 represents speed in miles per hour, and the variable "t" stands for time in hours.
To find the distance, you simply substitute the value of the time you have into the expression, replacing "t" with 5. The equation becomes:

• Distance = 400 × 5

By solving the expression, you find that the plane travels 2000 miles during the 5-hour flight.

Unit Conversion

Unit conversion is the process of changing a measurement to a different unit. This is key when working with measurements expressed in different units. In the context of speed and distance calculations, it's often necessary when comparing speeds or distances given in different units. For example, if you were converting speed from miles per hour to kilometers per hour, you would need to apply a conversion factor. The standard conversion factor is 1 mile = 1.60934 kilometers.
In this task, unit conversion isn't needed directly as both time and speed are already in compatible units (miles and hours), but knowing how to do it can be handy for other situations. Here's how you would convert the aircraft's speed of 400 miles per hour if necessary:

• Speed in kph = 400 mph × 1.60934 = 643.736 kph

Being proficient in unit conversion ensures you're flexible in handling various types of measurements in math and science.