You are a new member, which means there's a good chance that you did not consider the information in the post titled "Read Before Posting".
I will walk you through this first exercise, but I will not have much to say about the other two until you show some initiative.
On this first exercise, the answer is obviously not (e). The entire round trip took 30 hours; If he spent 30 hours walking back, that does not leave any time for driving! Since there are only four choices left, the quick way would be to start testing them to see which one is correct.
But, this exercise is for practicing algebra, so we should do some stuff with writing and solving an equation.
You need to know the following relationship; otherwise, you are not ready.
DISTANCE = RATE * TIME
In other words, we can express the length over which some object moves two different ways.
10 miles is one way to express a distance.
The product ( 5 miles/hour)*(2 hours) is another way to express the very same distance when we know that some object travels for 2 hours at a rate of 5 miles every hour.
If we do not know how much time elapsed for an object to travel some distance (call it d), but we know the rate (call it r), we can still write the distance by using a variable to represent the time.
t = elapsed time
r = 5 miles per hour
This is enough information to write an expression that represents the distance d:
5 * t
We don't know the actual number for d, but we could calculate it later after finding an actual value for t.
If t turns out to be 1 hour, then d is 5 miles.
If t turns out to be 7 hours, then d is 35 miles, and so on.
Remember! The expression r * t is the same as distance.
(But, d is not what this exercise wants.)
Once you understand the relationship d = r * t, then the first step for this word problem is to pick a variable to represent the very thing that the instructions ask for.
What are you supposed to find in this problem?
The instructions ask for the number of hours that Nathan walked. Pick a variable to represent this unknown elapsed time. Since it's a time, how about we use the standard symbol: t.
t = number of hours that Nathan spent walking
You're given the value of r that corresponds to this t. In other words, you're given 6 miles per hour for the rate.
So, now you should be able to write an expression that represents the distance d that Nathan walked.
Guess what?
d = the distance that Nathan drove, too. Right? (He drove the same distance that he walked.)
How do we express this same d using the rate and time for his drive?
The very same way: using new expressions to write rate * time.
You're given the rate at which he drove. Now write an expression (using the symbol t) for the driving time, and multiply it times the given rate.
How do you write an expression for the time spent driving?
We already said that t represents the time walking; if Nathan's round trip took a total of 30 hours, and he spent t hours walking, the difference between 30 and t must represent the amount of time driving.
Write an expression for this difference, and multiply it by the given driving rate.
Now you have two different products containing the variable t (one for the driving part and one for the walking part) which both represent the same distance traveled.
Since both products represent the same number, set them equal to one another, and you have an equation in one variable t.
Solve the equation for t using the algebra steps that you learned for solving equations in one variable.
Since t represents exactly what the exercise asks for (because we chose it to be so), you're done once you know its value. Find it in the list of multiple choices.
Please read the post titled "Read Before Posting", if you have not already done so. We like to see you make a start on each exercise, and try to say something about why you're stuck. This makes it much easier for us to see what kind of help you need without us having to type up a bunch of stuff that you may already know.
Don't fear making mistakes; mathematics proceeds by making mistakes and gaining experience.
So, if you need more help on this first exercise, please show us what you've done so far.
This is so easy if you know how to rationalize the denominator.
For example, if I rationalized the denominator for 17/?44, then I would get the following.
(17 * ?11)/22
Can you see the values for a, b, and c in this result corresponding to (a * Sqrt)/c ?
Clearly, their sum is 17 + 11 + 22.
Now, you do the same.
If you cannot remember the lesson given to you in class on how to rationalize the denominator, and you cannot find any lessons in a book or on the Internet, then let us know, and we will search the Internet for you.
I think that it would be better for you to look it up yourself; spend some time trying to learn how to rationalize the denominator.
If you do need more help with this exercise, then please show us what you've been able to come up with so far.
Since they are asking the question, then these three fractions must exist.
In other words, it's important to realize that we can assume the expression 4x^2 + y does not equal zero.
The exercise is asking whether or not this equation is a true statement.
Did you notice that the denominators in these three algebraic fractions are all the same?
Can you remember working with equations with simple fractions where all of the denominators are the same? What to do?
EG:
4a/b + 7a/b = 22a/b - 11a/b, with b ? 0
Is this equation true? Since all of the denominators are the same, we multiply both sides of the equation by the common denominator to clear the fractions.
4a + 7a = 22a - 11a
11a = 11a
It's true.
Now, you do the same.
If you need more help with this exercise, then please show your work so far, and try to say something about why you think you're stuck or unsure.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.
