SOLUTION: abby mows her neighbors' lawns during the summer in charlotte. Working alone she can mow all the lawns in 14 hours. If her brother helps her, they can mow all of the lawns in 8 h

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Question 1000: abby mows her neighbors' lawns during the summer in charlotte. Working alone she can mow all the lawns in 14 hours. If her brother helps her, they can mow all of the lawns in 8 hrs. How long would it take her brother to mow all of the lawns alone?
Found 3 solutions by KMST, MathTherapy, ikleyn:
Answer by KMST(5484) About Me  (Show Source):
You can put this solution on YOUR website!
Abby's lawnmowing task takes 14 hours, so she gets 1%2F14 of that task done on an hour.
If it would take her brother x hours to do the same task, he would get 1%2Fx of that task done in 1 hour.
Those are their "speeds".
Do you think her brother is faster or slower than Abby?
If they worked at the same "speed", how long would it take to do the same task working together?
Working together, they would get done 1%2F14%2B1%2Fx of that task in an hour, and would complete the whole 8%2F8=1 of that task in 8 hours.
So %281%2F14%2B1%2Fx%29%2A8=1 or %281%2F14%2B1%2Fx%29=1%2F8is the equation to solve for x .
We add those "fractions" using 14x as the common denominator 1%2F14%2B1%2Fx=1%2F8 <--> %28x%2B14%29%2F14x=1%2F8
Multiplying both sides times 8%2A14x , we get
8%28x%2B14%29=14x <--> 8x%2B112=14x
Subtracting 8x from both sides we get
112=14x-8x --> red%28112=%2814-8%29x%29 --> 112=6x (red step optional, unless your teacher want to see it)
Next, we divide both sides by 6 we get
112%2F6=x or x=112%2F6
Simplifying, we get x=56%2F3 .
That is how many hours it would take for Abby's brother to mow all of the lawns by himself.
Dividing we get 18 and a reminder of 3, sox=18%261%2F3 ,
but we know that one hour is 60 minutes and 1%2F3 hour is
%281%2F3%29%2A60=20 minutes.
It would take for Abby's brother 18 hours and 20 minutes to mow all of the lawns working alone.

Answer by MathTherapy(10897) About Me  (Show Source):
You can put this solution on YOUR website!
abby mows her neighbors' lawns during the summer in charlotte.  Working alone she can mow all the lawns in 14 hours. 
If her brother helps her, they can mow all of the lawns in 8 hrs.  How long would it take her brother to mow all of
the lawns alone?
****************
Abby completes the job in 14 hours, or 1%2F14 of job in 1 hour
Let time her brother takes to complete the job, ALONE, be B
Then, her brother can complete 1%2FB of job in 1 hour
As they both take 8 hours to complete the job, we get the following equation: 1%2F14+%2B+1%2FB+=+1%2F8
                                                                                                                                   4B + 56 = 7B ---- Multiplying by LCD, 56B
                                                                                                                                            56 = 7B - 4B
                                                                                                                                            56 = 3B
                                              Time her brother takes to complete the job, ALONE, or

Answer by ikleyn(54062) About Me  (Show Source):
You can put this solution on YOUR website!
.
Abby mows her neighbors' lawns in Charlotte during the summer. Working alone, she can mow all the lawns in 14 hours.
If her brother helps her, they can mow all of the lawns in 8 hours. How long would it take her brother to mow all
of the lawns alone?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        The post by @KMST contains an arithmetic error.
        So, I'm here to share a correct solution.
        I will not use equations, but will solve the problem in a simpler way, manipulating fractions. 


Abby does the whole job in 14 hours. 
Hence, Abby does 1%2F14  of the entire job in one hour.


Together, Abby and her brother do the whole job in 8 hours.
Hence, Abby and her brother do 1%2F8  of the whole job in 1 hour.


This implies that the brother's rate of work is the difference  1%2F8 - 1%2F14  of the job per hour.


This difference is  1%2F8 - 1%2F14 = %2814+-+8%29%2F%2814%2A8%29 = 6%2F%2814%2A8%29 = 3%2F%287%2A8%29 = 3%2F56.


So, the brother needs  56%2F3 hours = 18 2%2F3 hours = 18 hours and 40 minutes to complete the job working alone.


ANSWER.  The brother needs 18 hours and 40 minutes to mow all of the lawns.

Solved.