Hello, Bridget!
It's great to hear that you are eager to learn Algebra 1. Okay, so let me explain how you should approach these questions as I explain the solutions.
By the way, if you look at the Q&A section, there are some questions that have wrong answers, so make sure you read the Q&A sessions written by other students first, especially for Algebra 1, before you ask me a question because it might be redundant.
Now, let's get back to our questions!
Problem 4. Look at James. He finishes the question per hour. On the other hand, Rachel can finish one question within half an hour. For her, she can finish two questions per hour. So, within an hour, how many questions can they finish all together? I guess, they can finish three separate questions all together. So, given an hour, they finished three questions. Given 20 minutes, they are likely to finish one question.
Problem 5. Carter needs three hours to finish cleaning a classroom. So, per hour, Carter could only finish cleaning one third of the classroom. Jennifer, on the other hand, needs only an hour to do so. Jennifer could finish cleaning one classroom per hour. So, if they work together, they could clean one classroom + a third classroom per hour. That means, they can clean 4/3 classrooms per hour. Try to understand this way.
"4/3 classroom : 1 hour = 1 classroom : 3/4 hour (=45 minutes)!" So, they need 45 minutes to clean one classroom.
I think you did well for problem 6. But, for problem 7!
Let's look at it closely. Jung could finish the work in 11 hours. So if I give him one hour, he could finish 1/11 of the work. Same goes for James. If I give him an hour, he could finish 1/12 of the work. If they work together, then Jung could start working from the left corner of the field, while James could start working from the right corner of the field. They don't overlap!! So, after an hour, I found out that 1/11+ 1/12 of the work is done. So, this is the new workrate. 23/132 of the work per hour! That means, in order to finish one work, I need to give them 132/23 hours!
As I see your approach, you combine the rate in denominator and numerator all together. This complicates the issue. I hope you understood all the things I wrote down here. Try to come up with more of your own example and simulate the same process.
Enjoy studying!
