Two handymen can do a home repair in 2 hours if they work together. One of the men takes 3 hours more than the other man to finish the job by himself. How long does it take for each handyman to do the home repair individually?

Answers

Answer 1

Using the together rate, it is found that:

It takes 3 hours for the first handyman to do the home repair individually.It takes 6 hours for the second handyman.

The together rate is the sum of each separate rate.

In this problem, we have that:

The together rate is of [tex]\frac{1}{2}[/tex].The first man takes x hours, hence his rate is of [tex]\frac{1}{x}[/tex]The second man takes x + 3 hours, hence his rate is of [tex]\frac{1}{x + 3}[/tex]

Applying the together rate:

[tex]\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}[/tex]

[tex]\frac{x + 3 + x}{x(x + 3)} = \frac{1}{2}[/tex]

[tex]4x + 6 = x^2 + 3x[/tex]

[tex]x^2 - x - 6 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = -1, c = -6[/tex], hence:

[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-6) = 25[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{25}}{2} = 3[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{25}}{2} = -2[/tex]

We are interested into the positive root, then [tex]x = 3[/tex], [tex]x + 3 = 6[/tex], which means that:

It takes 3 hours for the first handyman to do the home repair individually.It takes 6 hours for the second handyman.

You can learn more about the together rate at https://brainly.com/question/25159431


Related Questions

the number obtained on rationalizing the denominator of 1/(√7--2) is

Answers

[tex] \frac{1}{ \sqrt{7} -(- 2)} \\ rationalizing \: \: \: the \: \: \: denominator \: \: \: we \: \: \: have \\ = \frac{1}{ \sqrt{7} + 2 } \times \frac{ \sqrt{7} - 2}{ \sqrt{7} - 2} \\ = \frac{ \sqrt{7} - 2}{ {( \sqrt{7} )}^{2} - {(2)}^{2} } \\ = \frac{ \sqrt{7} - 2 }{7 - 4} \\ = \frac{ \sqrt{7} - 2}{3} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Given that:

1/(√7 - 2)

The denominator is (√7-2).

We know

The rationalising factor of (√a-b) is (√a+b)

Therefore, the rationalising factor of √7-2 is √7+2.

On rationalising the denominator them

⇛[1/(√7-2)]×[(√7+2)/(√7+2)]

⇛[1(√7+2)]/[(√7-2)(√7+2)]

Since, (a-b)(a+b) = a²-b²

Where, a = √7 and b = √2.

⇛[1(√7+2)]/[(√7)²-(2)²]

⇛[1(√7+2)]/[(√7*7)-(2*2)]

⇛[1(√7+2)]/[7-4]

⇛[1(√7+2)]/3

⇛(√7+2)/3

Hence, the denominator is rationalised.

also read similar questions:

|-4+5x|=16
Pls help
Pls

Answers

Answer: i believe x = 4

Step-by-step explanation: 16 - |-4| which is adding two positives and that equals 20 so then its 5x = 20 divide 20 by 5 and you get 4

Find the length of the hypotenuse, side c, of a right triangle with legs of length a = 6 and b = 12.

Answers

Step-by-step explanation:

6²+12²

36 + 144 is 180

c=√180

The length of the hypotenuse is the square root of 180.

What is a length?

Length is defined as the measurement or extent of something from end to end.

Consider a right-angled triangle of two leg sides (a and b), and c is the third side (hypotenuse).

Given that a = 6 and b = 12,

The Pythagorean theorem states that

c^2 = a^2 + b^2

i.e. c^2 = 36 + 144

c^2 =180

Hence, the length of hypotenuse is square root of 180.

To learn more about length, use the link given below:

https://brainly.com/question/8552546

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how do i solve for this?

Answers

Step-by-step explanation:

1. KOL = 90

2.KLO = 25

3.NL= 30

4.KL = 17

workings

1.for angle

KOL =90 : the diagonals of rhombus are perpendicular to each other

2. angle LKO + angle KLO + angle KOL =180 : angles of triangle are supplementary(add to 180)

65+ KLO + 90 =180

KLO +155

KLO = 180 - 155

KLO = 25

3. NL = NO + LO: diagonals of the rhombus bisect each other

NL = 15 +15

NL = 30

4. Cos 25 = 15/KL

multiply by KL on both sides

KL × Cos 25 =15

divide by cos 25 on both sides

KL = 17

What is the sale price with 15% off? Original price: $110 of bears head phones

Answers

Answer:

93.5

Step-by-step explanation:

Nolan had 30 minutes to do a three-problem quiz. He spent 8 7/10 minutes on question A and 4 2/5 minutes on question B. How much time did he have left for question C?

Answers

Answer:

16 9/10 minutes

Step-by-step explanation:

She is solving 3 questions, so her total time spent =

Total time = Time spent on A + Time spent on B + Time spent on C

30 minutes = 8 7/10 + 4 2/5 + Time C

Time C = 30 minutes - (8 7/10 + 4 2/5)minutes

Time C = 30 minutes - (13 1/0 minutes)

Time C = 16 9/10 minutes

Answer: 16m 54s

Step-by-step explanation:

8 7/10 + 4 2/5 = 13 1/10 or 13m 6s

30m - 13m 6s = 16m 54s

Could i have Brainliest, I am trying to rank up

A bag of mixed nuts has 18 almonds, 8 cashews, and 14 peanuts. If one nut is selected, what is the probability that a peanut is chosen?

Provide the answer as a simplified fraction.

Answers

Answer:

7/20

Step-by-step explanation:

Answer:

ok so here is answer option no1

1/8 + 1/4 = 3/8

or you could do

18 plus 14 equals 32divided into 8 equals 4

Step-by-step explanation:

if this is wrong I'm very very very really really really sorry.

Don has seven pairs of​ shoes, three pairs of​ pants, and six shirts. If all items are​ compatible, how many different outfits can he​ wear?

Answers

Answer:

126

Step-by-step explanation:

There are 126 different ways he can wear the outfit.

What is Combination?

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.

Given:

Number of pairs of shoes= 7

Pants= 3 pairs

Shirts= 6

So, different outfits can he​ wear

= 7 x 3 x 6

= 21 x 6

= 126

Hence, there 126 different ways he can wear the outfit.

Learn more about combination here:

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Witch equation can be simplified to find the inverse of y=5x^2+10

Answers

Answer:

[tex]\huge\boxed{y=\sqrt{\dfrac{x-10}{2}}\ \text{for}\ x\geq10}[/tex]

Step-by-step explanation:

[tex]y=5x^2+10\\\\\text{exchange x to y and vice versa}\\\\x=5y^2+10\qquad|\text{subtract 10 from both sides}\\\\x-10=5y^2\qquad|\text{divide both sides by 5}\\\\\dfrac{x-10}{5}=y^2\\\\y^2=\dfrac{x-10}{5}\to y=\sqrt{\dfrac{x-10}{2}}[/tex]

Please help with this question

Answers

Answer:

D

Step-by-step explanation:

The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.

-hope it helps

Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.

Step-by-step explanation:


Solve x + 5x – 14 = 0

Answers

Hey there!

Solve the equation:

Answer :

x = 7/3 ✅

Explanations:

x + 5x - 14 = 0

>> Add 14 to both sides :

x + 5x - 14 + 14 = 0 + 14

x + 5x = 14

6x = 14

>> Divide each side by 6 :

6x / 6 = 14 / 6

x = 14/6

Simplify the result :

14 / 6 = 2*7 / 2*3 = 7/3

Therefore, your answer is 7/3 .

More about equations:

brainly.com/question/12058678

Have a good day :)

Yi = 4.0 + 1.5Xi
a. Interpret the Y intercept, b0.

Answers

Answer:

Divide each term in  Y i  =  4  +  1.5 X i  by  i  and simplify.

Y  =  −  4 i  +  1.5 X

Step-by-step explanation:

455,757,974,946,454 ×454,942,164,313,233.Plz help.​

Answers

91929229

7373738292929202010100110010110

satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?

Answers

4 x 6.5 = 26 revolutions

what is 5÷ 3 1/3 on khan academy

Answers

Answer:

1.5

Step-by-step explanation:

Hope this helped!

I need help with this, i did part of it but i'm desperate

Answers

Answer:

Let's add more steps.

step 6: angle AEB measures 360 - 90 -90 - 70 - 39 = 71° Reason, AECF is a quadrangonal and three of its angle measures 90, 90, and (70+39)

step 7: angles AEB and ABE are congruent: reason triangle ABE is isosceles since AE is conruent to AB

step 8 Angle BAE measures 180 -71-71 = 38°: by difference from the sum of the internal angles.

step 9: Angle BAD measures 90 - BAE = 90 - 38 = 52° Reason angles BAD and BAE are complementary.

QED

(9/5)^3

I have no idea

Answers

Answer:

5.832

Step-by-step explanation:

The weight of 120 books is 36kg, find the weight per book

Answers

Answer:

0.3kg

Step-by-step explanation:

Since the weight of 120 books is 36kg, the weight per book will be:

= 36kg / 120

= 0.3kg

What is the perimeter, in feet, of the polygon?

Answers

Step-by-step explanation:

please post the question correctly to get the answer.

Question: What is 32^2?

Answers

Answer: The answer is 1,024.

Explanation: 32^2 is 32 x 32, which is 1,024.

1,024

Explanation: calculator

1. A store in Grand Rapids, Michigan, advertised a side-by-side

refrigerator for $1,699.99.

a. What is the sales tax if the combined state and city rate is 6%?

b. What is the total purchase price?

Answers

The store  Grand Rapids in Michigan placed and advert for a refrigerator for $1,699.99, also the tax rate is 6%.

Total cost = Tax + cost of refrigerator

$2719.984

Solution

let us find 6% of $1,699.99, this will be the amount paid as tax

Tax = 6/100*$1,699.99

Tax = 0.6*1,699.99

Tax = $1019.994

Now let us find the total amount paid for the refrigerator

This will be the cost of the refrigerator plus the Tax paid

Total = 1,699.99+1019.994

Total = $2719.984

Learn more about Tax here

https://brainly.com/question/25783927

Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units left and 2 units
down on the parent function f(x)=x^2

Answers

Answer: The graph for x cubed has a steep incline levels for a little before another steep incline

explanation: Since choice B is the only one that looks like this the answer is B

help please please help​

Answers

Answer:

24/35

Step-by-step explanation:

Hope this helps!:)

What is the equation, in point-slope form, for a line that goes through (2, – 6) and has a slope of -3/4?

y-6 = 3/4 (x-2)

y–6=-3/4(x+2)

y+6= -3/4 (x+2)

y+6= -3/4 (x– 2)

Answers

Answer:

y+6=-3/4(x-2)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-6)=-3/4(x-2)

y+6=-3/4(x-2)

Graph the equation 2x - y = -3

PLEASE HELP, I HAVE NO IDEA HOW.

Answers

Step-by-step explanation:

Lets assume that x=0

Therefore- 2×0-y= -3

                0 - y =-3

Therefore y = -3

Then lets take now the before equation

2x - 3= -3

2x = -3+3

2x=0

x=0÷2

∴ x= 0

Answer is- 0,-3

See image

You have to change the equation so it's in the form y=mx+b.

b is the y-intercept and it is a good starting point and m is the slope and it tells you directions to the next point (also how steep or flat and if it's going up or down) See image

2. A football is kicked in the air and its height, in metres, is given by the function h(t)=−4.9t^2+19.6t+1 , where t is measured in seconds.

a) determine the time it took to reach the maximum height

b) determine the maximum height of the ball

Answers

Answer:

27

Step-by-step explanation:

A tree is 6 feet 7 inches tall. How tall is it in inches?

Answers

Answer:

79 inches

Step-by-step explanation:

1 foot equals 12 inches

6 feet = 6*12 = 72 inches

72+7=79

79 inches


Three different sets of objects contain 2, 3, and 14 objects, respectively. How
many unique combinations can be formed by picking one object from each
set?
A. 28
B. 42
C. 84
D. 19

Answers

the answer is C, eighty four combinations

Answer:

C) 84

Step-by-step explanation:

Use the Fundamental Counting Principle, which states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. In this case, we have 2 ways to select one object from the first set, 3 ways to select one object from the second set, and 14 ways to select one object from the third set. So, we multiply and do 2*3*14=84

Therefore, there are 84 unique combinations

find the perimeter of the triangle A(4,-2) B(9,-2) C(9,10)

Answers

Answer:

  30 units

Step-by-step explanation:

A graph can help you see the lengths of the sides. This is a right triangle, so the length of the hypotenuse is found using the Pythagorean theorem:

  5² +12² = b² = 169

  b = √169 = 13

The perimeter is 5+12+13 = 30 units.

2 1/2+x=5 1/3 PLEASE HELP

Answers

Answer:

Step-by-step explanation:

2 1/2 + x = 5 1/3                Change the mixed numbers to improper fractions

5/2 + x = 16/3                   The lowest common multiple is 6. Multiply by 6

5*3 + 6x = 16*2

15 + 6x = 32                      Subtract 15 from both sides.

6x = 32 - 15

6x = 17                              Divide by 6

6x/6 = 17/6

x = 2 5/6

Check

5/2 + 17/6 = 16/3

15/6 + 17/6 = 32/6

32/6 = 32/6                    The question checks.

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