Can you please help me with these Algebra word problems?
Complete the following word problems.
1. Tell whether the table represents inverse variation. If so, write the inverse variation equation and solve for y when x = 4. Show work that supports your conclusions.
Table:
Amperes (x): 310, 124, 62, 15.5
Ohms (y): .04, 0.1, 0.2, 0.8
2. It takes 9 hours for Isabella to rake leaves by herself, but her brother Matthew can work three times as fast. If they work together, how long will it take to rake leaves?
Thank you for your help.
Without actually checking, I'd have to say it better be yes. (Ohm's Law).
Having said that, since amps*ohms is constant,
4y = .1*124
y = 3.1
Sure, I can help you with these algebra word problems. Let's start with the first one.
1. To determine whether the table represents inverse variation, we need to check if the product of the x-values and the y-values is constant. Let's calculate this product for each row of the table:
For the first row, 310 * 0.04 = 12.4
For the second row, 124 * 0.1 = 12.4
For the third row, 62 * 0.2 = 12.4
For the fourth row, 15.5 * 0.8 = 12.4
Since the product is constant for all rows, this table does represent inverse variation.
To find the inverse variation equation, we can use the general form: y = k/x, where k is the constant of variation.
Let's use the first row to solve for k:
0.04 = k/310
To isolate k, multiply both sides of the equation by 310:
k = 0.04 * 310
k = 12.4
So the inverse variation equation is y = 12.4/x.
Now, let's solve for y when x = 4:
y = 12.4/4
y = 3.1
Therefore, when x = 4, y = 3.1 is the solution to the equation.
Moving on to the second word problem:
2. Isabella takes 9 hours to rake leaves by herself, and her brother Matthew works three times as fast. Let's denote Matthew's time to complete the task as t.
If they work together, their combined work rate is the sum of their individual work rates. Since Isabella takes 9 hours, her work rate is 1/9 of the task per hour. Matthew, who works three times as fast, has a work rate of 3/9 or 1/3 of the task per hour.
To find how long it takes to complete the task together, we can add their rates:
1/9 + 1/3 = (1/9 + 3/9) = 4/9
The combined work rate is 4/9 of the task per hour. To find the time it takes to complete the task together, we need to find the reciprocal of the combined work rate. The reciprocal of 4/9 is 9/4.
Therefore, it will take them 9/4 hours to rake leaves together, which simplifies to 2.25 hours or 2 hours and 15 minutes.
I hope this helps! Let me know if you have any further questions.