The first stage of a rocket burns 28 s longer than the second stage. If the total burn time for both stages is 152 s, how long does each stage burn? Describe how you found your answer.

I was originally thinking to divide 152 by 2 then add 28, but I realized that wouldn't work and now I'm lost. Any help is appreciated, thank you!

First Stage = x + 28, second = x

x + 28 + x = 152

Solve for x, then x + 28.

time of burn of 2nd stage = x seconds

time of burn of 1st stage = x+28

x + x+28=152
2x = 124
x = 62

2nd stage takes 62 seconds
1st stage is x+28 = 62+28 = 96 sec

To find the burn time for each stage, let's start by assigning variables to represent the burn times of the first and second stages. Let's say the burn time for the second stage is x seconds.

According to the problem, the first stage burns 28 seconds longer than the second stage. So, the burn time for the first stage can be represented as (x + 28) seconds.

The total burn time for both stages is given as 152 seconds. Therefore, we can set up the following equation:

x + (x + 28) = 152

Now, let's solve for x to find the burn time of the second stage:

2x + 28 = 152 (combine like terms)
2x = 124
x = 124/2
x = 62

So, the burn time for the second stage is 62 seconds.

To find the burn time for the first stage, we can substitute the value of x back into our expression:

Burn time for the first stage = x + 28 = 62 + 28 = 90 seconds

Therefore, the first stage burns for 90 seconds, and the second stage burns for 62 seconds.

To summarize:
- First stage burn time: 90 seconds
- Second stage burn time: 62 seconds

This method involved setting up equations based on the given information and solving for the unknown variables to find the answer.