Q45. - Algebra 1

Question

Speedometer accuracy can be affected by many details such as tire diameter and axle ratio. For example, there is variation of $\pm 3$ miles per hour when calibrated at 50 miles per hour.

1. What is the range of actual speeds of the car if calibrated at 50 miles per hour?
2. A speedometer calibrated at 45 miles per hour has an accepted variation of $\pm$ mile per hour. What can we conclude from this?

Step-by-Step Solution

Answer

1.  The range of actual speeds of the car if calibrated at 50 miles per hour is 47 to 50 miles per hour.
2. The speedometer is more accurately calibrated than the speedometer of part a, many factors could affect the calibration of a speedometer and cause one speedometer to be more accurate than another.

Part a. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, constant are the values which is fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part a. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Part a. Step 3. Solution along with the given information.

Line 1: Variation of $\pm 3$ miles per hour when calibrated at 50 miles per hour. 

Line 2: Car calibrated at 50 miles per hour.

 

The range of actual speed of the car if calibrated at 50 miles per hour is to be found.

Consider, the speed of the car is x.

According to the question,

$\left|x-50\right|=3$ 

Case 1: $\left(x-50\right)=3$

Add 50 to both sides of the equation.

 $\begin{array}{l}x-50+50=3+50\\ x+0=53\\ x=53\end{array}$

 

Case 2: $\left(x-50\right)=-3$

$\begin{array}{l}x-50+50=-3+50\\ x+0=47\\ x=47\end{array}$ 

 

Therefore, the range of actual speeds of the car if calibrated at 50 miles per hour is 47 to 50 miles per hour.

Part b. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation constant are the values which is fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part b. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Part b. Step 3. Solution along with the given information.

Line 1: Variation of $\pm 3$ miles per hour when calibrated at 50 miles per hour. 

Line 2: Car calibrated at 45 miles per hour has an accepted variation of $\pm 1$ mile per hour. 

 

Calculation:

The conclusion for a speedometer calibrated at 45 miles per hour has an accepted variation of $\pm 1$ miles per hour is to be made.

Therefore, the speedometer is more accurately calibrated than the speedometer of part a, many factors could affect the calibration of a speedometer and cause one speedometer to be more accurate than another.