after a heavy thunderstorm, the rodriguez familys garage had 6 inches of rain in that was being pumped out at a rate of 0.50 inches per hour. the smith family had 14 inches of rain in their garage being pumped out at a rate of 1.5 inches per hour. how many hours will it take fr the water level at the smiths garage to be equal to or less than the rodriguezs

Let's define variables for the problem:

- Let \( t \) represent the number of hours after the pumping starts.
- The Rodriguez family has 6 inches of water, and it is being pumped at a rate of 0.50 inches per hour. So, after \( t \) hours, the water level in their garage will be:
  \[
  6 - 0.50t
  \]
- The Smith family has 14 inches of water, and it is being pumped at a rate of 1.5 inches per hour. So, after \( t \) hours, the water level in their garage will be:
  \[
  14 - 1.5t
  \]

We want to find when the water level in the Smith family's garage will be equal to or less than the water level in the Rodriguez family's garage. This gives us the inequality:
\[
14 - 1.5t \leq 6 - 0.5t
\]

### Solving the inequality:

1. Subtract \( 6 \) from both sides:
   \[
   14 - 1.5t - 6 \leq -0.5t
   \]
   Simplifying:
   \[
   8 - 1.5t \leq -0.5t
   \]

2. Add \( 1.5t \) to both sides:
   \[
   8 \leq t
   \]

Thus, it will take **8 hours** for the water level in the Smith family's garage to be equal to or less than the water level in the Rodriguez family's garage.

### Conclusion:
After 8 hours, the water in the Smith family’s garage will be equal to or less than the water in the Rodriguez family’s garage.

Would you like more details on any step? Here are some related questions to consider:

1. How would the equation change if the pumping rates were different?
2. What if the Rodriguez family's garage had more initial water than the Smiths'?
3. Can you solve for the exact water levels after a certain time?
4. How would the time change if both families increased their pumping rates?
5. What happens if the initial water levels were the same for both families?

**Tip:** Always check units (inches per hour in this case) to make sure the rate of change is consistent throughout the problem.

After a heavy thunderstorm, the Rodriguez family's garage had 6 inches of rain that was being pumped out at a rate of 0.50 inches per hour. The Smith family had 14 inches of rain in their garage being pumped out at a rate of 1.5 inches per hour. How many hours will it take for the water level at the Smiths' garage to be equal to or less than the Rodriguez's?

Learn how to solve a real-world problem using linear inequalities: compare water levels in two garages after a heavy storm with different pumping rates. This problem covers algebraic concepts, including linear equations and inequalities. Suitable for students in Grades 6-8.

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