A tank has 120 gallons of water and is being drained at a rate of  1over2
  gallon each second. Another tank has 100 gallons of water and is being drained at a rate of  1over4
  gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?

We are given two tanks, each being drained at different rates, and we want to find the number of seconds \( x \) when both tanks have the same amount of water.

### First Tank:
- Initial amount of water: 120 gallons
- Draining rate: \( \frac{1}{2} \) gallon per second
- After \( x \) seconds, the amount of water left in the first tank will be:
  \[
  120 - \frac{1}{2}x
  \]

### Second Tank:
- Initial amount of water: 100 gallons
- Draining rate: \( \frac{1}{4} \) gallon per second
- After \( x \) seconds, the amount of water left in the second tank will be:
  \[
  100 - \frac{1}{4}x
  \]

To find when the two tanks have the same amount of water, we set the two expressions equal to each other:
\[
120 - \frac{1}{2}x = 100 - \frac{1}{4}x
\]

This equation can now be solved for \( x \), the number of seconds when both tanks have the same amount of water.

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Would you like me to solve this equation or provide more details?

### Related Questions:
1. How do you solve for \( x \) in the equation \( 120 - \frac{1}{2}x = 100 - \frac{1}{4}x \)?
2. What happens if the second tank is draining faster?
3. How would the equation change if the initial water levels were different?
4. What is the interpretation of \( x = 0 \) in this context?
5. What would happen if both tanks were draining at the same rate?

**Tip:** When setting up word problems involving rates, make sure to write an equation that represents the situation step by step.

A tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second. Another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?

This problem involves finding when two tanks, one with 120 gallons draining at 1/2 gallon per second and another with 100 gallons draining at 1/4 gallon per second, will have the same amount of water. Learn to set up and solve a linear equation step by step. Suitable for Grades 7-9.

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