Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.
We will find that working together, they need to work for 8 hours.
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Let's start by defining the variables that we will use:
A = rate at which Aran worksB = rate at which Beatrice works.C = rate at which Charlie works.Now let's see the given information:
"Aran and Beatrice can build an ant hill in 10 hours"
This can be written as:
(A + B)*10 h = 1 ant hill
"Aran and Charlie can build the ant hill in 12 hours"
This can be written as:
(A + C)*12 h = 1 ant hill
"Beatrice and Charlie can build the ant hill in 15 hours"
This can be written as:
(B + C)*15 h = 1 ant hill.
Then we have 3 equations:
[tex](A + B)*10 h = 1[/tex]
[tex](A + C)*12 h = 1[/tex]
[tex](B + C)*15 h = 1[/tex]
Where for commodity, I removed the "ant hill" unit.
Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.
I will isolate A in the first equation:
[tex]A = \frac{1}{10h} - B[/tex]
Now we can replace it in the second equation to get:
[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]
Now we can isolate C in the last equation to get:
[tex]C = \frac{1}{15h} - B[/tex]
Replacing that in the above equation we get:
[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]
This means that Beatrice alone would construct the hill in 24 hours.
Now that we know the value of B, we can use:
[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]
This means that Charlie needs 40 hours to finish the hill alone.
Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:
[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]
Now if the 3 ants work together, the total rate at which they work is:
[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]
This means that they need to work for the inverse of that rate
[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]
Working together, they need to work for 8 hours to complete an ant hill
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HURRY
1/12 is the same as 1÷12. What is the exact quotient in decimal form of 1÷12?
Answer: Yes 1/12 is the same as 1 ÷ 12
decimal form is 0.083333333333333333(3 is repeating)
Step-by-step explanation:
Answer:
0.08333333333
Step-by-step explanation: since i helped can i have brainlist please :D
Guys help I’ve been trying to solve this problem for the past 40 minutes.
Answer:
56 degrees since you set the two equations equal to each other and then plug the value of p (which is 11) back in to find the answer.
I need to write an equation for the triangle and solve for x
2x + y = 11
3x - y = 4
Answer:
[tex]x=3,y=5[/tex]Step-by-step explanation:
Add the equations together and solve for x.
[tex](2x + y )+ (3x - y) = 11 + 4[/tex]
[tex]5x=15[/tex]
[tex]x=3[/tex]
Use equation [tex]2x+y=11[/tex] to solve for y.
[tex]2(3) +y=11[/tex]
[tex]6+y=11[/tex]
[tex]y=11-6[/tex]
[tex]y=5[/tex]
Re write the statement 19+7 divided by 2-5 by including one pair of brackets to make the total equal to 8
PLS HELP I'LL MARK BRAINLEST
Answer:
a
Step-by-step explanation:
180-50
Hey there!
Hope this helps!
x=130
Help me with this circle question
Answer:
50.265482457436 inches
Step-by-step explanation:
radius = 8 inches
C = 2×pi×r
= 2×pi×8
C = 50.265482457436 inches
Need Help with this please!!
Answer:
A is 85 degrees
please solve for b
a=b/c
Answer:
b = ac
Step-by-step explanation:
Solve for b by simplifying both sides of the equation, then isolating the variable.
Answer:
b= ac
Solve for b by simplifying both sides of the equation, then isolating the variable.
hello My name es Liliana y arigato bye
Answer:
?????.... hii erica herrrr
Answer:
Hi Liliana i love your name! it's very pretty:) my name is Melody
Step-by-step explanation:
What is the measure of angle P?
Answer:
60
Step-by-step explanation:
step 1: 180°-130°= 50
step 2: 180-110= 70
step 3: 70+50= 120
step 4: 180°-120°= 60
14 is 33 1/2% of what number?
Answer:
41.79
Step-by-step explanation:
c = 14 * 100/33.5 = 1400/33.5 = 2800/67
= 41.79104
which of the following numbers is irrational
Answer:
E
Step-by-step explanation:
Irrational means cannot be put into a fraction. Or random repeating decimals is how I remember it.
√48 can be simplified to equal 4√3. √3 cannot be put into fraction form.
Determine the intercepts of the line x-intercept
Answer:
I dont know if you meant where it intercepts the x line or y line so for the x line it intercepts at -7.5 but for y line it intercepts at 5.5
at a concession stand three hotdogs in for hamburgers cost $13.50 for hotdogs and three hamburgers cost $12.75 find the cost of one hotdog and find the cost of one hamburger
What is the image of the point (3,2)(3,2) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin?
Answer: = (-2,3)
Step-by-step explanation:
Rotation is a transformation of a figure by rotating it for a specific angle about a fixed point.Here, fixed point = origin = (0,0)
Transformation rule for rotation of [tex]90^{\circ}[/tex]counterclockwise about the origin:
[tex](x,y)\to (-y,x)[/tex]
Then, the image of the point (3,2) = (-2,3)
Hence, the image of the point (3,2) after a rotation of [tex]90^{\circ}[/tex]counterclockwise about the origin = (-2,3)
Answer: The answer is -2,3 because 90 degrees of the orgin :) enjoy
Step-by-step explanation:
pls dont say random stuff to get points
Answer:
C) 3 1/4
Step-by-step explanation:
Juan received a bank account statement reporting the recent changes
to his account. The statement showed an overall increase in the
account balance of $1,909.15. During the time shown on the
statement, Juan was paid twice and withdrew a total of $1,437.99 to
cover all his bills and expenses. How much (x) is each of Juan's
paychecks?
Answer:
2628.15
Step-by-step explanation:
1909.15+ 1437.99/2=2628.15
Number seven plz helppp
Answer:
1,296
Step-by-step explanation:
I multiplied 6 four times.
Kim drew a map of the Mississippi River. The scale was 5 centimeters represents 120 miles. The actual length of the Mississippi River is 360 miles. Approximately what is the length in centimeters of the Mississippi River on the map?
50 points to who ever answer it corectly
Answer:
15 cm on the map
Step-by-step explanation:
360/120=3
5*3=15
hope this helps :)
need help plz help me
Answer:
The last one t/5-6=-3
Step-by-step explanation:
All you have to do is plug in 15 to each equation, knowing this if you add 15 into this equation you would get 15/5-6=-3 and this is true because 15/5=3, 3-6=-3!
I hope this helps and have a great day!
Help pleas brainliest promise
Answer:
1) 13
2) 1
Step-by-step explanation:
1) you add the e amount of people that went to the store 3 and 5 times because those are all more than 2.
2) 1 has the lowest number on the amount of landings.
Solve the system.... 2y+8x+58 and y-5x=11
Answer:
x=2, y=21
Step-by-step explanation:
there are two methods: substiution and elimation. I will be doing subtistution in this soultion:
first isolate y in either equation, it would be easier to do it in the second one.
y= 11+5x
Then, subtitute that into the first equation
2(11+5x)+8x=58 (it says 2y+8x+58 but I assume you mean 2y+8x=58?)
22+10x+8x=58
18x = 36
x=2
substitute that back into y = 11+5x, to get y=11+10 = 21
If GEOM is a square, find m2GQE.
Answer:
90 is correct answer of it question
What is the value of j?
___°
34 degrees.
If you want to find how much an angle is, first check the original line (aka base). Then (only if the line is a 180 degree line) subtract whatever value is shown (in this case it was 146 degrees so what you would do is subtract 146 from 180 and you would have your answer).
Hope this helps.
-Northstar
What hazard is present in this image?
Select the best option.
A mat that has upturned edges
Hair clippings on the floor
Tool cord left out
Spills on floor
Answer:
spills on the floor
Step-by-step explanation:
there is liquid of some sort someone could slip and hurt themselves. hope this helps
How many times will the graph of this equation cross the x-
axis?
y= 22^2– 7x - 9
can someone please help me?
reduce to the simplest form[tex]\frac{286}{858}[/tex]
Answer:
143 over 428
Step-by-step explanation:
-x + 7y = 8 if x equals 6
Answer:
y=2
Step-by-step explanation:
-6+7y=8
7y=8+6
7y=14
y=2