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
statuscvo [17]
3 years ago
12

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor

k together they can do the entire prospectus in five hours. How long will it take each of them working alone to repair the prospectus? Round answers to the nearest 10th of an hour
Mathematics
1 answer:
Dahasolnce [82]3 years ago
3 0

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

<u>Solution:</u>

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is \frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }

If they work together they can do the entire prospectus in five hours

\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}

On cross-multiplication we get,

\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}

\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}

On cross multiplication ,we get

\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}

<em><u>using quadratic formula:-</u></em>

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

x=\frac{12 \pm \sqrt{144-40}}{2}

\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

You might be interested in
These 12 shapes are put into a bag. If you reach
Svetlanka [38]
25 times :) hope this helped!
3 0
2 years ago
HELP PLEASE!! Identify the solution set of the inequality using the given replacement set. x &lt; –2; {–5, –2.6, –2, –0.8, 1, 1.
UNO [17]
X< -2 means that x must be smaller than -2, so something like -3, -4, -5, etc

The only solution set that fits this is A.
6 0
3 years ago
Really need help, thanks in advance!
Bond [772]

Answer:

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Which values of x make this equation true?
Evgesh-ka [11]

Answer:

{x}^{2}  + x = 12 \\  {x}^{2}  + x - 12 = 0 \\  {x }^{2}  + 4x - 3x - 12 = 0 \\ x(x + 4) - 3(x + 4) = 0 \\ (x + 4)(x - 3) = 0 \\ either \:  \:  \: or \:  \\ x =  - 4 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: x = 3

the answer is -4 and 3

3 0
2 years ago
How would the equation
hammer [34]

Answer:

what

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • Correct?<br><br> ...Which quadratic regression equation best fits the data set?
    7·1 answer
  • Find the greatest common factor of x^2y and xy^2
    7·1 answer
  • Which of the following statements is true about a graph that is perfectly symmetric, such as the one above?
    6·2 answers
  • A square garden has an area of 100ft^2.what is the length of each side of the garden
    12·1 answer
  • 1 2/5 x 3/5 in lowest terms please
    6·1 answer
  • When taking skinfold measurement readings only one attempt per site is necessary for an accurate reading.a. Trueb. False
    15·1 answer
  • HELP
    13·1 answer
  • Can someone help me please!!!
    14·2 answers
  • Plz help as many times as i try i still don't get it
    9·2 answers
  • Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!