It takes an older employee 13 hours to shovel the snow from a sidewalk, but a younger employee can shovel the same sidewalk in 10 hours. how long will it take them to clear the walk if they work together?
Time taken by both of the older employee and younger employee is 5.6 hrs
What is Componendo-dividendo rule?Componendo-dividendo rule: A theorem based on the topic of proportions permits a faster way to carry out the calculations and cut down the count of expansions required. It is helpful in situations involving equations with fractions or rational functions. The componendo and dividendo rule are used while studying ratios and proportions. If the ratio of any two given numbers is the same as the ratio of the other 2 numbers, then the ratios of the sum total of the numerator and denominator to the difference of the numerator and denominator of the two rational numbers are equal in nature.
Given, older employee needs 13 hours to shovel the snow.
So in 1 hr the older employee will shovel = 1/13
Younger employee needs 10 hours to shovel the snow.
So in 1 hr the younger employee will shovel = 1/10
Now, when they work together
[tex]1/13+1/10 = 1/x \\(10+13)/130 = 1/x \\3/130 = 1/x\\x = 130/23 = 5.6 hrs[/tex]
Hence, the time taken by both of them together is 5.6 hrs
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Final answer:
Two employees working together can clear the sidewalk in approximately 6 hours and 31 minutes. This is determined by finding the individual work rates, combining them, and then taking the reciprocal of the combined rate to find the total time worked together.
Explanation:
To find out how long it will take two employees to shovel snow together, we need to determine their combined work rate. The older employee takes 13 hours, and the younger employee takes 10 hours. First, we calculate each of their work rates per hour by taking the reciprocal of their time.
So, the older employee's work rate is 1/13 sidewalks per hour and the younger employee's 1/10 sidewalks per hour. To find their combined work rate, we add these two rates together:
Combined work rate = (1/13) + (1/10) = (10 + 13) / (13 × 10) = 23/130 sidewalks per hour
Now, to find the total time taken to shovel the sidewalk when working together, we take the reciprocal of the combined work rate:
Time taken working together = 1 / (23/130) = 130/23 hours
To make this more interpretable, we can convert it into a mixed number:
Time taken working together = 5 hours and (130/23 - 5 × 23/23) hours = 5 hours and 35/23 hours
We can convert 35/23 hours into minutes by multiplying by 60:
Additional minutes = (35/23) × 60 minutes = approximately 91 minutes
Therefore, the time taken working together is roughly 5 hours and 91 minutes, which simplifies to 6 hours and 31 minutes.
Lukas graphed the system of equations shown. 2x + 3y = 2 y = x + 3 What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)
The solution to the given system of linear equations is (-1.4, 1.6).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are 2x+3y=2 -----(i) and y=x+3 -----(ii)
Substitute, equation (ii) in equation (i), we get
2x+3(x+3)=2
2x+3x+9=2
5x=-7
x=-7/5
x=-1.4
Substitute x=-1.4 in equation (ii), we get
2(-1.4)+3y=2
-2.8+3y=2
3y=2+2.8
3y=4.8/3
y=1.6
So, the solution is (-1.4, 1.6)
Therefore, the solution to the given system of linear equations is (-1.4, 1.6).
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Identify the standard form of the equation by completing the square
the price of a television decreased from 1000.00 to 800.00.what is the percent of decrease.
Answer:
The decrease is 20%
Step-by-step explanation:
In a horse race, how many different finishes among the first 33 places are possible if 20 horses20 horses are running? (exclude ties)
To solve this problem, let us break this down one by one.
There are 20 possible
horses that could win in first place. Therefore this means that for each of
these possibilities, there are now 19 horses that could come in second. So
meaning there are 20 x 19 possible combinations for the first 2 places.
20 x 19 = 380. And for each of those combinations, there are also
18 possible horses that could come in the third place. So
20 x 19 x 18 = 6,840
There are 6,840 possible horse combinations for the first 3
places in the race.
What is the factorization of the polynomial below?
x^3-4x^2+45x
The graph represents a person's heart rate in beats per minute during 30 minutes of exercise.
Which statement best describes the relationship between heart rate and time doing exercise?
Looking at the graph closely we can see that the heart rate increases from 0 to 6 min then became steady from 6 to 25 min then finally decreases from 25 to 30 min. Therefore the correct answer is:
“The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.”
In real life cardiac exercises, we can interpret that the period from 0 to 6 min is the period where the person is still warming up thus leading to an increase in heart rate. At 6 min, the person is fully warmed up hence reaching a stable heart rate. Then at 25 min, the person starts cooling down which means that the exercise is ending soon.
3/5x+19−3/20x−7/35x+19−3/20x−7 simplified is
Final answer:
To simplify the expression, combine like terms and then simplify to get (1/4)x+24.
Explanation:
To simplify the expression, 3/5x+19−3/20x−7/35x+19−3/20x−7, we can combine like terms and then simplify:
Combine 3/5x−3/20x−7/35x to get (3/5−3/20−7/35)x = (12/20−3/20−4/20)x = (5/20)x = (1/4)x.Combine 19+19 to get 38.Combine −7−7 to get −14.Combine the results: (1/4)x+38−14 = (1/4)x+24.So, the simplified expression is (1/4)x+24.
Can some one please help me with this question answer What is 40%of 320
If a weighted score for a project is based on just two criteria, fit with strategy, weighted 70% and roi, weighted 30%, what would be the weighted score for a project with scores of 80 on fit with strategy and 50 on roi?
Final answer:
To calculate the weighted score for a project, apply the weights to the scores for each criterion and sum the results. The calculated weighted score for a project with scores of 80 on 'fit with strategy' (70% weight) and 50 on 'ROI' (30% weight) is 71.
Explanation:
To calculate the weighted score for a project based on the provided criteria, you need to apply the weights to the scores for each criterion and then sum the results. In this case, the criteria are 'fit with strategy' which has a weight of 70% and 'ROI' which has a weight of 30%.
The weighted score for 'fit with strategy' is calculated as follows:
(Score for 'fit with strategy' × Weight of 'fit with strategy') = (80 × 0.7) = 56.
The weighted score for 'ROI' is calculated as follows:
(Score for 'ROI' × Weight of 'ROI') = (50 × 0.3) = 15.
To find the total weighted score for the project, you add these two results together: 56 (from fit with strategy) + 15 (from ROI) = 71.
Therefore, the total weighted score for the project is 71.
What is the graph of x = -5?
Which Act protects consumers against inaccurate and unfair practices from credit card companies and lenders? The ______ in Lending Act protects consumers against inaccurate and unfair practices from credit card companies and lenders.
Answer:
Truth
Step-by-step explanation:
[tex]-2y + y - 3 = 6
[/tex]
Felicia put $175 into a CD that pays 4% interest, compounded semiannually. According to the rule of 72, approximately how long will it take for her money to double?
Answer:
the answer is 18 years
Step-by-step explanation:
i just did this on 12/8/18 good luck to cheaters
PLEASE HELP NEED ASAP! 10 PTS!
Solve each system by elimination.
1. -9x+2y= -1.
18x-7y=17
2. 4x+18y= -28
2x+9y= -14
3. 20x+y= -11
-10x-3y= -17
4. -3x+y=7
-6x+2y=12
Thank you!
Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π? (?
Manuel and rita bought cds at the music store. rita's cds originally cost three times more than manuel's cds, but she received a $9 discount. if rita spent $21 total, which equation can be used to find the amount manuel spent
Answer with Step-by-step explanation:
Let cost of Manuel's cds=m
Rita's cds originally cost three times more than Manuel's cds, but she received a $9 discount.
i.e. Rita's cds cost=3m-9
Rita spent $21 total.
i.e. 3m-9=21
Adding 9 on both sides, we get
3m=30
Dividing both sides by 3, we get
m=10
Hence, equation which can be used to find the amount Manuel spent is:
3m-9=21
Explain 2 other ways other than rotating 180 degrees counterclockwise or clockwise, that would allow the point to find it’s way to the same place from its original position. Hint: You may combine transformations.
"It was you who awoke me last summer out of a life-long stupid dream" write the conclusion for this quote
What is the answer to
-18= 117/p-9
I NEED THIS ANSWER NOWWWW PICTURE ATTACHED
Which system of inequalities is represented by the graph?
y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1
a ratio is a rate, sometimes,never, or always?
The graph shows the location of Jacob's, Kent's, and Hakim's houses. Each unit on the graph represents 1 kilometer. A coordinate plane is shown. Hakims house is located at negative 3, 1, Jacobs house is located at 1, 5, and Kents house is located at 1, 1. Line segments connect the points to form a right triangle.
Answer:
14 km
Step-by-step explanation:
I did FLVS
A geometric sequence has a common ratio of 2/9 and the first term is 729 what is the 8th term?
A card is drawn from a standard deck of 52 cards. what is the probability that it is a heart? type in your answer to two decimal places!
How to divide fractions with whole numbers
If the problem is 7+(-5) how many spaces do you move to the right or left
Solve the equation using square roots. x^2-15=34
Find the area of a rectangular almond orchard that is 200 yards long and 100 yards wide.
300 square yards
2100 square yards
2000 square yards
20000 square yards
In a restaurant there are 3 choices for appetizers, 6 choices for entrees, and 4 choices for desserts. How many different meal choices are there if you were to have 1 appetizer, 1 entree, and 1 dessert?
24
72
13
18