Water: Middle School
Exercise II. The Superior Car Wash
How Much Water Does It Take?
It takes 25 gallons of water for a 5-minute shower and 35 gallons to fill a normal bathtub. In comparison, the average person washing a car uses more than 500 gallons of water! All that water and the suds from car shampoo washes down the street's storm drain into the waterways. Over time car wash runoff adds up to some serious "personal" pollution!
Making a Superior Car Wash-Doing the Fractional Math
The exercise below suggests how you can make a superior car wash - superior in terms of not only car cleaning but also water pollution reduction.
Imagine that you have a weird bucket that holds as much as you want, but no matter how hard you try, you can never empty the last ounce when you drain it. In your weird bucket, there is now 1 undrainable ounce of some sort of gunk you want to rinse away.
Start out with 1 ounce of gunk in your bucket. Draw it!
Do the math!
Mix in 1 ounce of water. You now have a 2-ounce mixture of gunk and water. Drain away half of the mixture. How much total mixture is left? How much of that is water? How much of it is gunk?
Repeat. Pour in an ounce of water so that you have a 2-ounce mixture. Drain away half of the mixture. How much gunk do you have now?
Repeat again. After three dilutions, how much gunk is left?
Suppose you want to get down to 1/8 ounce of gunk by adding water just once to your weird bucket. How much water will you need to add?
Making a Superior Car Wash-Thinking It Through
How many total ounces of water did the one-big-wash method take?
How many ounces of water did the small-repeated-washes method take?
Which method is better? Explain your answer.
Putting It All Together
When you wash your car, soap attaches to the dirt and loosens the hold the dirt has on the car. This makes it easier for water to rinse away the dirt. If you were to closely examine the water left on your car after rinsing it, you would find a thin layer of water containing dirt with soap attached to it.
Think of the dirt with soap attached as the gunk talked about in the questions above. If you rinse your car with just enough water to cover the surface of the car, it acts like diluting the gunk with water as you did in the examples above. Each time you add water and drain the mixture, you are left with a smaller amount of soapy dirt gunk still in the mixture than you had before. If this mixture works the same way as the mixture in the weird bucket, which method would use less water - one big rinse or several small rinses?
Think about this the next time you wash your car. You can use less water if you use several small rinses instead of one large one.