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bearhunter [10]
3 years ago
14

It takes Emily eight hours to paint her house. Mike can paint the same area in nine hours. Find how long it would take them if t

hey worked together.
7.58 hours

15.34 hours

3.56 hours

4.24 hours
Mathematics
2 answers:
Olenka [21]3 years ago
7 0

<u>Answer:</u>

It would take them 4.24 hours if they worked together.

<u>Explanation:</u>

We are given that

time taken by emily to paint her house = 8 hours and

time take by Mike to paint the same area = 9 hours

We have to find the time taken by them if the work together, let this be x so x will be given by,  

\frac{1}{8}+\frac{1}{9}=\frac{1}{x}

\frac{9+8}{72}=\frac{1}{x}

x=\frac{72}{17}

= 4.24 hours

which is the time taken by Emily and Mike to paint the house when they do it together.

emmasim [6.3K]3 years ago
4 0

It will take them 4.24 hours together to paint the area together

Step-by-step explanation:

If Emily takes eight hours to paint the area then she will paint 1/8 of the house in one hour

Similarly, if Mike can paint the same area in 9 hours, then he will paint 1/9 of the same area

Let x be the number of hours in which they will together paint the area.

If x hours are taken by them to paint the area then 1/x of the area will be painted in one hour

So,

\frac{1}{8}+\frac{1}{9}=\frac{1}{x}\\Multiplying\ both\ sides\ with\ the\ LCM\\72x\\(72x)*\frac{1}{8}+(72x)*\frac{1}{9}=72x * \frac{1}{x}\\9x+8x=72\\17x=72\\Dividing\ both\ sides\ by\ 17\\\frac{17x}{17}=\frac{72}{17}\\x=4.24\ hours

It will take them 4.24 hours together to paint the area together

Keywords: Linear equation, Variables

Learn more about linear equations at:

  • brainly.com/question/10772025
  • brainly.com/question/10879401

#LearnwithBrainly

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Answer:

Y=ax2

Step-by-ste:

Y=ax28(n)

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Oscar needs to purchase soft drinks for a staff party. He is
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2 years ago
PLEASE HELP
katrin2010 [14]

The game that is  used for the scenario above in terms of fair play is  using a balloon. Here, the player will hit the balloon.

<h3>What is the scenario under the balloon game?</h3>

The rule of play are:

This is a classic game with simple rules which are:

  • Each player to hit the balloon up and it bonce into the air but when one should not allow it to touch the ground.,
  • Players would be tied together in twos and they will juggle a lot of balloon and it have to be more than 1 balloon with one of their hands tied to their back.

A scenario of the worksheet game whose expected value is 0 is given below:

Assume that it costs about $1 for a player to play the billon game and as such, if  the player hits a balloon, they will be given $3. what can you say. Can you say that it this game is fair or not? and who has the biggest advantage.

Solution

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4 0
2 years ago
A cable television compan is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides
Schach [20]

Answer:

Step-by-step explanation:

Given:

Point Q = Q is on the north bank 1200 m east of P $40/m to lay cable underground and $80/m way to lay the cable.

Lets denote T be a point on north bank, therefore, point T is t m east and 100m north of P.

Note that 0 < t < 1200

Distance from P to T using Pythagoras theorem:

PT^2 = PQ^2 + QT^2

PT = √(t²+100²) = √(t²+10,000)

Distance from T to Q:

TQ = 1200 - t

From above, Cable from P to T is underwater, and costs $80/m to lay.

Cable from T to Q is underground, and costs $40/m to lay.

Total cost of the cable:

C(t) = 80√(t²+10,000) + 40(1200 - t)

Cost is at its minimum: when dC/dt = C'(t) = 0 and d^2C/dt^2 = C''(t) > 0

dC/dt = C'(t)

= 80 * 1/2 (t² + 10,000)^(-1/2) × 2t + 40 × (-1)

dC/dt = C'(t)

= 80t/√(t² + 10,000) - 40 = 0

80t/√(t² + 10,000) = 40

80t = 40√(t² + 10,000)

2t = √(t² + 10,000)

square both sides:

4t² = t² + 10,000

3t² = 10,000

t² = 10,000/3

t = 100/√3

≈ 57.735

d^2C/dt^2 =

C''(t) = [80√(t² + 10,000) - 80t × t/√(t²+10,000)] /√(t²+10,000)

C''(t) = [(80(t²+10,000) - 80t²) / √(t²+10,000)] /√(t²+10,000)

C''(t) = 800,000 / (t² + 10,000)^(3/2)

C''(t) > 0 for all t

Therefore C(t) is minimized at t = 100/√3

C(100/√3) = 80√(10,000/3 + 10,000) + 40 × (1200 - 100/√3)

= 80 √(40,000/3) + 48,000 - 4000/√3

= 16000/√3 + 48,000 - 4000/√3

= 48,000 + 12,000/√3

= 48,000 + 4,000√3

= 4000 (12 + √3)

≈ 54,928.20

Minimum cost is $54,928.20

This occurs when cable is laid underwater from point P to point T(57.735 m east and 100m north of P) and then underground from point T to point Q (1200 - 57.735)

= 1142.265 m

5 0
3 years ago
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Answer:

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h(5) = 23

8 0
3 years ago
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