1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ivann1987 [24]
3 years ago
8

Ben, Tim, and Sam have to do a certain job. Ben can finish the job in 5 hours. Tim can finish the job in 6 hours. Sam can finish

the job in x hours. The three of them can finish the job in 2 hours if they work together. Find x.
Mathematics
1 answer:
Brut [27]3 years ago
5 0

x is 7.5 hours

Step-by-step explanation:

Ben, Tim, and Sam have to do a certain job

  • Ben can finish the job in 5 hours
  • Tim can finish the job in 6 hours
  • Sam can finish the job in x hours
  • The three of them can finish the job in 2 hours if they work together

We need to find x

∵ Ben can finish the job in 5 hours

∴ The rate of Ben = \frac{1}{5}

∵ Tim can finish the job in 6 hours

∴ The rate of Tim = \frac{1}{6}

∵ Sam can finish the job in x hours

∴ The rate of Sam = \frac{1}{x}

They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2

∵ They can finish the job in 2 hours if they work together

∴ \frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}

To add the fractions find the LCM for all denominators to make all fractions with same denominators

∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,

- Divide it by each denominator to find the new numerators

∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30

- Change all the denominators to 30 x and then write the new

   numerators of each fraction

∴ \frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}

Add the numerators and put the sum over 30 x

∵ \frac{11x+30}{30x}=\frac{1}{2}

- By using cross multiplication

∴ 2(11 x + 30) = 1(30 x)

- Simplify the both sides

∴ 22 x + 60 = 30 x

- Subtract 22 x from both sides

∴ 60 = 8 x

- Divide both sides by 8

∴ 7.5 = x

∴ The value of x is 7.5 hours

x is 7.5 hours

Learn more:

You can learn more about the word problems in brainly.com/question/10712420

#LearnwithBrainly

You might be interested in
Find the probability that the family of 3 children will have exactly 2 girls
SOVA2 [1]
Well if we're talking genetics included in the answer its 3/8
5 0
3 years ago
Question#1 Please simplify..
riadik2000 [5.3K]
Hey there,
6x + 5 (x-2)
6x + 5x - 10
11x - 10

3x - 5 - x + 9 
3x - x - 5 + 9
2x + 4

3a + 5 - 8a + 1
3 (-1) + 5 - 8(-1) + 1
-3 + 5 + 8 + 1
11

Hope this helps :))

<em>~Top♥</em>

5 0
3 years ago
Drag the tiles to the correct boxes to complete the pairs. Match each system of inequalities to the graph representing its solut
mojhsa [17]

The solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)

<h3>How to determine the solution to the systems?</h3>

The graph of the systems of inequalities is not given.

So, I would plot a new graph to answer this question.

The systems of inequalities are given as:

y − x > 1 and 2x + y ≤ 2

x + y ≥ -3 and 5x – y ≤ -3

2x – y ≤ -1 and x + 2y < 4

4x – 3y < 12 and x + 3y ≥ 6

Next, we plot these inequalities on a graph and write out the points of intersection.

From the attached graph, we have:

y − x > 1 and 2x + y ≤ 2  ⇒ (0.3, 1.3)

x + y ≥ -3 and 5x – y ≤ -3  ⇒ (-1, -2)

2x – y ≤ -1 and x + 2y < 4  ⇒ (0.4, 1.8)

4x – 3y < 12 and x + 3y ≥ 6 ⇒ (3.6, 0.8)

Hence, the solutions to the systems of inequalities are (0.3, 1.3), (-1, -2), (0.4, 1.8) and (3.6, 0.8)

Read more about systems of equations at:

brainly.com/question/21405634

#SPJ1

8 0
1 year ago
On a number line what is the distance between -12 and 20 ??
KIM [24]

Answer:  Step-by-step explanation:

In order to answer this question you will need to find 2 distances and then add them to each other.

Begin at -29.  How far will you have to move to the right 29 in order to get to 0?

Now how far will you have to more to get from 0 to 100?

Draw an open number line to help you.

_____________________________________________________

-29                                           0                                                   100

Your first distance is 29.  Your second distance is 100.  The total distance is 129.

3 0
3 years ago
90/9 as a whole number
stiks02 [169]

Answer:

10

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Which is the graph of linear inequality 2x-3y&lt;12 ?
    14·2 answers
  • Find the volume of the resulting solid if the region under the curve y = 7/(x^2 + 5x + 6) from x = 0 to x = 1 is rotated about t
    11·1 answer
  • PLEASE HELP!!!! I know the answer, but I don’t know how to solve the problem!!!
    13·1 answer
  • Manny was given the equation (x+2)(x-7)=0 and asked to find the zeros. The solutions he came up with were x=2 and x=-17.
    15·1 answer
  • 7n +2 –(2n +7) pls help I will give you 15 points
    11·1 answer
  • Chang family is on way home from a cross country road trip. Are they driving for 18 hours or do they have 18 hours to go?
    13·1 answer
  • Help me with this :////
    9·1 answer
  • NEED HELP WITH PART B ASAP!
    7·2 answers
  • Profit is the difference of revenue and cost. Assuming the costs are $150, write an equation that represents the revenue R from
    8·1 answer
  • Pleaseee hurry and answer
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!