Q68. - Algebra 1

Question

John’s mother has agreed to take him driving every day for two weeks. On the first day, John drives for 20 minutes. Each day after that John derives 5 more minutes more than the day before

1. Write an expression for the nth term. Explain how you found the expression.
2. For how many minutes will Jhon drive on the last day?
3. John’s driver’s education teacher requires that each student drive for 30 hours with an adult outside of class. Will John’s sessions with his mother fulfill this requirement?

Step-by-Step Solution

Answer

1. The expression for the nth term driving by John is $20+5n$.
2. John would drive 85 minutes on the last day.
3. John’s session will not fulfill his requirement.

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, the constants are the values that are fixed.

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

Part a. Step 2. Given information.

John’s mother has agreed to take him driving every day for two weeks. On the first day, John drives for 20 minutes. Each day after that John drives 5 minutes more than the day before. John’s teacher requires that each student drive for 30 hours with an adult outside of class.

Part a. Step 3. Solution for the given information.

Consider the question

Each day, John will drive an additional 5 minutes.

For $n$ days, John will drive $5n$.

And first day he drove 20 minutes.

So,

The expression becomes $20+5n$ because John will drive 20 minutes on the first day and then an additional 5 minutes for each day after that.

 

Therefore, the expression for the nth term driving by John is width="53" style="max-width: none; vertical-align: -4px;" $20+5n$.

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, the constants are the values that are fixed.

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

Part b. Step 2. Given information.

John’s mother has agreed to take him driving every day for two weeks. On the first day, John drives for 20 minutes. Each day after that John drives 5 minutes more than the day before. And John’s teacher requires that each student drive for 30 hours with an adult outside of class.

Part b. Step 3. Solution for the given information.

The total number of days that John drives is 14.

Since the first day is considered to be 0^th day. So, substituting the value $n=13$ in the equation $20+5n$.

$$\begin{gathered} M=20+5n \\ =20+5\left(13\right) \\ =20+65 \\ =85 \end{gathered}$$ 

 

Therefore, John would drive 85 minutes on the last day.

Part c. 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, the constants are the values that are fixed.

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

Part c. Step 2. Given information.

John’s mother has agreed to take him driving every day for two weeks. On the first day, John drives for 20 minutes. Each day after that John drives 5 minutes more than the day before and John’s teacher requires that each student drive for 30 hours with an adult outside of class.

Part c. Step 3. Solution for the given information.

The time taken by John’s driver teacher is $t=30$ hours

$$\begin{gathered} t=30\times 60\text{ minutes} \\ t=1800\text{ minutes} \end{gathered}$$ 

Calculate the time taken by John

$20+25+30+35+40+45+50+55+60+65+70+75+80+85=735$ 

So, John will take 735 minutes.

Therefore, John’s session will not fulfill his requirement.