You put water in the hot tub, after x minutes is the depth y cm where y=40+0,5x how many minutes until the water is 120cm

The relationship between the depth of the water \( y \) and the time \( x \) is given by the equation:

\[
y = 40 + 0.5x
\]

We want to find the time \( x \) when the depth of the water \( y \) is 120 cm. To do this, substitute \( y = 120 \) into the equation:

\[
120 = 40 + 0.5x
\]

Now, solve for \( x \):

1. Subtract 40 from both sides:
   \[
   120 - 40 = 0.5x
   \]
   \[
   80 = 0.5x
   \]

2. Divide both sides by 0.5:
   \[
   x = \frac{80}{0.5}
   \]
   \[
   x = 160
   \]

So, it will take **160 minutes** for the water to reach a depth of 120 cm.

Would you like more details on how this was solved, or do you have any questions?

Here are 5 related questions:
1. What happens if you change the rate at which the tub fills to 1 cm per minute?
2. How would the equation change if the initial depth was different?
3. What if you want to stop the water at 150 cm? How long would that take?
4. How does the depth increase over time affect the volume of water?
5. What if there is a leak in the tub? How would that affect the equation?

**Tip:** Always ensure units are consistent when solving real-world problems (e.g., depth in cm, time in minutes).

You put water in the hot tub, after x minutes is the depth y cm where y=40+0.5x. How many minutes until the water is 120cm?

Discover how to calculate the time it takes for the water depth in a hot tub to reach 120 cm using the linear equation y = 40 + 0.5x. This step-by-step solution explains how to solve the equation and provides additional related questions. Suitable for students in Grades 6-8.

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