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
VLD [36.1K]
3 years ago
8

Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th

e carpets in 2 hours. How long would it take Henry to clean the office carpets if Mary were not there to help?
Mathematics
1 answer:
Sati [7]3 years ago
8 0

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is \frac{1}{t}

∵ The rate of Mary is \frac{1}{t+3}

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by \frac{1}{2} (their rate together)

∴ \frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ \frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}

∴  \frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}

- Add the two fractions in the left hand side

∴ \frac{t+3+t}{t(t+3)}=\frac{1}{2}

∴  \frac{2t+3}{t^{2}+3t}=\frac{1}{2}

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

OR

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

You might be interested in
37% of women consider themselves fans of professional baseball. you randomly select six women and ask each if she considers hers
valina [46]

Answer:

(a) 2.22

(b) 1.3986

(c) 1.183

Step-by-step explanation:

Let <em>X</em> denote the number of women who consider themselves fans of professional baseball.

The proportion of women who consider themselves fans of professional baseball is, <em>p</em> = 0.37.

A random sample of <em>n</em> = 6 women are selected and each was asked if she considers herself a fan of professional baseball.

Each woman's reply is independent of the others.

The random variable <em>X</em> thus follows a binomial distribution with parameters <em>n</em> = 6 and <em>p</em> = 0.37.

(a)

Compute the mean of the binomial distribution as follows:

\text{Mean}=np=6\times 0.37=2.22

(b)

Compute the variance of the binomial distribution as follows:

\text{Variance}=np(1-p)=6\times 0.37\times (1-0.37)=1.3986

(c)

Compute the standard deviation of the binomial distribution as follows:

\text{Standard Deviation}=\sqrt{np(1-p)}=\sqrt{6\times 0.37\times (1-0.37)}=1.183

5 0
2 years ago
A dice is rolled and a marble is selected at random from a bag with 2 red marbles, 2 green marbles, 2 yellow marbles, 1 purple m
laila [671]
1/3 times 6/8

1/3 times 3/4

So, the answer is 3/12

Simplify: 1/4
4 0
3 years ago
carly tutors stufents in math on the weekends and offers both thirty minute and sixtyminute sessions she earns $15for each thirt
Ronch [10]

Answer:

X=7

Step-by-step explanation:

7*15=105 7-2=5 5*25=125 125+105=230

6 0
3 years ago
The measure of an angle is 78°. What is the measure of a complementary angle?
ki77a [65]
First you need to know the definition of a complementary angle. That means that two angles add up to 90 degrees, or a right angle.

To find an angle complementary to a 78 degree angle, you need to subtract 78 from 90. 

90 - 78 = 12
6 0
3 years ago
Read 2 more answers
The square root of 125 is between what two numbers
Otrada [13]

The square root of 125 is in between 11 and 12. It is 11.1803.

6 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP 20 POINTS AND WILL MAKE BRAINLIEST!!!!
    9·1 answer
  • The temperature was -3*C on Friday and dropped overnight by 9*C. What was the temperature on Saturday morning
    13·1 answer
  • Convert 0.875 inch to a fraction in simplest form. Click to select the correct answer.
    10·1 answer
  • Can someone help Me ? I suck at Riemann sums in general
    11·1 answer
  • Find the points of intersection (if any) of the graphs of the equations. Use a graphing utility to check your results. y = - x +
    12·1 answer
  • What is the solution to the system of equations below?<br> y=-3/2x+6<br> y= 5x - 7
    6·1 answer
  • ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎
    9·1 answer
  • So easy
    15·2 answers
  • 127°<br> 37°<br> Х<br> Calculate the size of angle x.<br> angle x =
    11·1 answer
  • Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!