The Choi family has two sprinkler systems. Combined, the two systems have a water output rate of 45 L per hour. Last summer, the first system was used for 35 hours, and the second system was used for 20 hours. There was a combined total output of 1200 L of water. What is the water output rate for each system? First sprinkler system: Second sprinkler system: \( \square \mathrm{L} \) per hour

Let's say the water output rate of the first sprinkler system is \( x \) L per hour, and the second sprinkler system is \( 45 - x \) L per hour. From the usage data, we can set up the equation based on the total water output: \[ 35x + 20(45 - x) = 1200 \] Expanding this gives us: \[ 35x + 900 - 20x = 1200 \] This simplifies to: \[ 15x + 900 = 1200 \] Subtracting 900 from both sides: \[ 15x = 300 \] Now, dividing both sides by 15, we find that: \[ x = 20 \] So, the first sprinkler system has an output of \( 20 \) L per hour. For the second system: \[ 45 - x = 45 - 20 = 25 \] The water output rate for each system is: First sprinkler system: \( 20 \mathrm{L} \) per hour Second sprinkler system: \( 25 \mathrm{L} \) per hour Understanding how efficient irrigation systems work can improve water conservation. Historically, sprinkler systems have evolved from primitive manual systems to sophisticated automated ones. Today, advancements, such as smart watering technology, allow homeowners to monitor and adjust their systems based on weather forecasts, ensuring plants receive just the right amount of water without waste. To avoid common pitfalls in calculating water usage, double-check your variables! It's easy to mix up the hours or rates. Always validate your assumptions and equations, especially when dealing with multiple systems. Using clear labels and organized calculations can save headaches and errors down the line!