Harry can rake the leaves in the yard 8 hours faster than his little brother jimmy can. if they work together, they can complete the job in 3 hours. using complete sentences, explain each step in figuring out how to determine the time it would take jimmy to complete this job on his own.

Explanation:

1. Analyze the problem to identify what is given and what is asked for. We are asked for the time it takes Jimmy to complete a job. We are given a relation between Jimmy's time and his brother's time, and we are also told the time when they work together.

2. Choose a variable or set of variables that will help answer the question when the value(s) of the variable(s) is(are) found. Here, it is convenient to assign a variable to Jimmy's time, as finding the value of that will answer the question. We can call that variable "j". (It is often helpful to use variables with names that help you remember what they stand for. It is easy to confuse the meanings of generic variables such as "x" and "y".)

3. Write the relations given in the problem statement as an equation or set of equations. Here, we need to realize that when two people work together, their rates of doing work are added. Those rates, in terms of jobs per hour, are the reciprocal of the job completion times in hours per job.

Since Harry's time to complete the job is 8 hours less than Jimmy's we can use (j-8) to represent it. Then the total job completion rate in jobs per hour is ...

  1/j + 1/(j-8) = 1/3

4. Solve the equation using the rules of algebra. Here, we can clear fractions by multiplying the equation by the product of the denominators:

  3(j -8) +3j = j(j -8)

Eliminate parentheses and collect terms:

  3j -24 + 3j = j^2 -8j

  -24 = j^2 -14j

Complete the square by adding the square of half the j coefficient.

  -24 +49 = j^2 -14j +49

  25 = (j -7)^2

Take the positive square root. We know that j must be greater than 8+3, so time values less than 7 will not make sense in this problem.

  5 = j -7

Add 7.

  12 = j

5. Using the value(s) of the variable(s) found, formulate an answer to the question. Here, that answer is ...

  It would take Jimmy 12 hours to complete this job on his own.

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages