a machine fills 150 bottles of water every 8 minutes. How many minutes will it take this machine to fill 675 bottles?

Question

 I want a description of how to answer this question in order to help a child in a math class so I can help him or her better understand the question.

Answer 1

Math-wise, this is a proportions problem.

 

150 bottles / 8 minutes = 675 bottles / how long?

 

When you solve the proportion, the answer is the time (in minutes) it takes to fill the 675 bottles. (In this case, 36 minutes.)

 

Concept-wise, it's a little tougher. Because of questions the kids ask:

• Why do I need 675 bottles?
• How do we use this in real life? (I wish I had a dollar for every time I've heard that one.)

 

What I have to tell them is that we have devices that measure things, but the measurement they give us is not always (not usually, seldom, almost never) the answer to a question we have.

• I know how fast the car goes. So how long will it take me to get home?
• I know how much time I have to work on the test. So how many problems will I be able to answer? How many do I have to skip?

 

The answers to those kinds of questions are rooted in proportion problems. A proportion is how we take what we know about a process and use that information to find out something we don't know but want to know. For whatever reasons.

 

I hope that helps. Cheers!