Chapter 12.1, Problem 25STP

To determine

To calculate: Number of seconds in the first stage.

Answer to Problem 25STP

Number of seconds in the first stage = $90$

Explanation of Solution

Given information:

The first stage of a rocket burns $28\text{ seconds}$ longer than the second stage.

Total burning time = $\text{152 seconds}$

Calculation:

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

The first stage is $\text{28 seconds}$ longer than the second stage.

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

  $\begin{array}{l}\text{Total burning time is 152 seconds [Words]}\\ x+x+28=152\text{ [Equation]}\end{array}$

The equation can be solved as follows:

  $\begin{array}{l}x+x+28=152 [\text{Original equation]}\\ x+28=152\text{ [Add like terms]}\\ \underset{\_}{-28=-28} [\text{Subtract 28 from both sides]}\\ 2x=124\text{ [Simplify]}\\ \frac{2x}{2}=\frac{124}{2} [\text{Divivde 2 from both sides]}\\ x=62 [\text{Simplify]}\end{array}$

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