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bazaltina [42]
3 years ago
9

Jeff and Kirk can build 75 feet retaining wall together in 10 hours. Because Jeff has more experience, he could build the wall b

y himself 1 hour quicker than Kirk. How long would it take Kirk to build the wall by himself.
Mathematics
1 answer:
frez [133]3 years ago
7 0
Let J and K be the times of Jeff and Kirk respectively
To know the time it takes two people to perform a task together use the equation:
\frac{1}{J}+ \frac{1}{K}= \frac{1}{10}
We also know from the problem that J=K-1, so
\frac{1}{K-1}+ \frac{1}{K}= \frac{1}{10}

Now get common denominators
\frac{K}{K(K-1)}+ \frac{K-1}{K(K-1)}= \frac{1}{10}
\frac{K+K-1}{K(K-1)}= \frac{1}{10}
Take reciprocals
\frac{K(K-1)}{2K-1}=10
K(K-1)=10(2K-1)
K^{2} -K=20K-10
K^{2} -21K+10=0
By the quadratic equation:
K=20.512
J=K-1=19.512
Putting these into the original formula for two people working together on a task
\frac{1}{20.512}+ \frac{1}{19.512}= \frac{1}{10}
So it checks out.
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Elvira and Aletheia live 3.1 miles apart on the same street. They are in a study group that meets at a coffee shop between their
Sophie [7]

Answer:

  • Elvira's speed: 3.0 mph
  • Aletheia's speed: 2.4 mph

Step-by-step explanation:

Let "e" and "a" represent the speeds of Elvira and Aletheia, respectively. Then the total distance they cover is ...

  distance = speed × time

  (1/2)e + (2/3)a = 3.1

And the relationship between their speeds is ...

  e - a = 0.6

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To solve this system, we can double the first equation and subtract the second to get ...

  2(1/2e +2/3a) -(e -a) = 2(3.1) -(0.6)

 7/3a = 5.6 . . . . . . . . . . simplify

  a = (3/7)(5.6) = 2.4 . . . multiply by 3/7

  e = a +0.6 = 3.0 . . . . . Elvira's speed is 0.6 mph more than Aletheia's

Elvira's walking speed is 3.0 miles per hour; Aletheia's is 2.4 miles per hour.

7 0
3 years ago
A restaurant offers 10 appetizers and 12 main courses. In how many ways can a person order a​ two-course meal? Use the Fundament
aliya0001 [1]

Answer:

80 ways

Step-by-step explanation:

The first thing is to apply the Fundamental Counting Principle with two groups of items, in this case the multiplication rule is used.

In this case, what we should do is that, for every 1 main course there are 8 appetizers, but there are 10 main courses therefore:

8 * 10 = 80

There are 80 ways to combine appetizers and the main course

5 0
3 years ago
Where did the formula of sphere comes from
Elina [12.6K]

Answer:

Archimedes was the first to derive this formula.

Step-by-step explanation:


7 0
3 years ago
Write a irrational number between 1/8 and 3/5​
hjlf

Answer:

answer is 1/8

Step-by-step explanation:

hope this helps

3 0
3 years ago
I need help um i dont need to to my work or check my answer just
romanna [79]
3.
area=legngth tiimes width
legnth is 10 more than 2 times width
l=10+2w
lw=area=(10+2w)w=10w+2w^2
area=3600
3600=10w+2w^2
so divide by 2
1800=5w+w^2
subtract 1800 from both sides
(note they used x instead of w)
0=w^2+5w-1800
then the facotred form is (w-40)(w+45)=0

0 product property measn if you have xy, then x and or y =0

therefor
w-40=0 and w+45=0
w=40 or -45
discard negative because negative legnth is not possible


explian how solution relates to situation
it is math so it is correct because we represented it corrrectly


the other solution is because of math and eliminate negative legnth becasue tha tis not possible
basically because we represented it correctly
not a very clear quetion to answer

basically 'because it represents the solution so we solved it and it is correct'


8 0
3 years ago
Read 2 more answers
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