Problem 14 - Intermediate Algebra

Question

Flying the SR-71A jet, Capt. Elden W. Joersz USAF, set a record speed of 2193.16 miles per hour. At this speed. the algebraic expression \(2193.16 t\) gives the total distance flown in \(t\) hours Find the distance flown by the SR-71A in 1.7 hours.

Step-by-Step Solution

Answer

The distance flown by the SR-71A in 1.7 hours is 3728.372 miles.

Step 1: Understand the Problem

The problem asks us to calculate the total distance flown by the SR-71A jet in 1.7 hours, given that its speed is 2193.16 miles per hour. The algebraic expression for the distance flown is given by \(2193.16 \times t\).

Step 2: Substitute the Given Value

Substitute the given time, \(t = 1.7\) hours, into the expression for the distance, which is \(2193.16 \times t\). This gives us \(2193.16 \times 1.7\).

Step 3: Calculate the Distance

Perform the multiplication to find the distance. Calculate \(2193.16 \times 1.7\) to find the total distance flown.

Step 4: Solve the Multiplication

Calculate the expression \(2193.16 \times 1.7 = 3728.372\). Thus, the total distance flown by the SR-71A in 1.7 hours is 3728.372 miles.

Key Concepts

Distance Calculation in Algebraic Expressions

Calculating distance using algebraic expressions is a straightforward process. Distance calculation often involves relations between speed, time, and distance itself in mathematical terms.
In this example, the speed of the jet is given as 2193.16 miles per hour, and we have a specific time duration, 1.7 hours. To determine the total distance, an algebraic expression is utilized:

• The distance flown, represented as a mathematical product of speed and time, is given by the expression \(2193.16 \times t\).

This approach takes advantage of the simple mathematical principle that distance equals speed multiplied by time.
Therefore, to calculate how far the jet travels, simply substitute the value of time into the given expression. This method efficiently computes distances when provided with constant speeds over defined intervals.

Understanding Multiplication in Algebra

Multiplication is a fundamental arithmetic operation often used in algebraic expressions to express relationships between quantities.
In the SR-71A jet problem, the expression \(2193.16 \times t\) is crucial. Multiplication here represents combining the speed (2193.16 mph) with the duration of the flight (in hours).

• It's the process of repetitive addition. For instance, multiplying 2193.16 by 1.7 sums up the distance covered each hour to the total journey distance in 1.7 hours.
• This specific operation involves multiplying a decimal (2193.16) by another decimal (1.7), which can initially seem complex but follows the same principles as regular number multiplication.

Calculators or manual calculation methods help find the result efficiently and accurately, illustrating how multiplication translates expressed relationships into tangible numbers.

Role of Variables in Algebraic Expressions

Variables serve as placeholders in algebraic expressions, representing generic values that can change. They make mathematical expressions versatile and broadly applicable to various situations.
In our exercise, the variable \(t\) signifies time in hours, creating a flexible model for distance calculations that can accommodate different values of \(t\).

• By substituting specific numerical values into \(t\), like 1.7 in our example, we convert abstract expressions into concrete calculations.
• This allows algebraic calculations to be adapted to measure new scenarios, reflecting the dynamic relationship between speed and time.

The use of variables makes it easier to adjust calculations, facilitating a deeper understanding of mathematical dynamics and adaptability in real-world applications.