Q25. - Algebra 1

Question

The first stage of a rocket burns 28 seconds longer than the second stage. If the total burning time is 152 seconds, how many seconds is the first stage?

Step-by-Step Solution

Answer

The number of seconds in the first stage is 90.

Step 1. State the concept for observational studies.

The linear equations in one variable is an equation which is expressed in the form of $ax+b=0$, where $a$ and $b$ are two integers, and $x$ is a variable and has only one solution.

Step 2. Form the equation .

Let the number of seconds in the second stage be $x$

The first stage is 28 seconds longer than the second stage.

Therefore, the number of seconds in the first stage in $x+28$ seconds.

$$\begin{gathered} \text{Total burning time}=152\text{ seconds} \\ x+x+28=152 \end{gathered}$$

Step 3. Solve the equation.

The equation can be solved as follows:

$$\begin{gathered} x+x+28=152 \\ 2x+28=152 \\ 2x+28-28=152-28 \\ 2x=124 \\ \frac{2x}{2}=\frac{124}{2} \\ x=62 \end{gathered}$$

Number of seconds in the first stage $=x+28=62+28=90$.

Therefore, the number of seconds in the first stage is 90 seconds.