anonymous
  • anonymous
Jackson takes 6 hours to clean the garage alone,but can clean it in 1.5 hours if he works with Mary.how long does it take Mary to clean the garage if she works alone
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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whpalmer4
  • whpalmer4
how many garages can Jackson train per hour?
whpalmer4
  • whpalmer4
finding unit rates is an easy approach to solving such problems.
anonymous
  • anonymous
I don't quite understand how to solve it

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More answers

whpalmer4
  • whpalmer4
Okay, if Jackson takes 6 hours to clean 1 garage, what is his unit? How many garages (or fractions of a garage) does he clean in 1 hour?
whpalmer4
  • whpalmer4
\[\frac{1\text{ garage cleaned}}{1 \text{ hour}} = \frac{1}{6} \frac{\text{garages cleaned}}{\text{hour}}\]right?
whpalmer4
  • whpalmer4
sorry, that should have been 6 hours in the denominator of the left hand fraction! \[\frac{1\text{ garage cleaned}}{6 \text{ hours}} = \frac{1}{6} \frac{\text{garages cleaned}}{\text{hour}}\]
whpalmer4
  • whpalmer4
That is the "unit rate" for Jackson clean garages. If he has 6 hours, he can clean 6*(1/6) = 1 garage. In 12 hours, he can clean 12*(1/6) = 2 garages. In 3 hours, he can clean 3*(1/6) = 1/2 of a garage, etc.
whpalmer4
  • whpalmer4
Clear so far?
whpalmer4
  • whpalmer4
How much of a garage does Jackson get done working on his own for 1.5 hours?
anonymous
  • anonymous
Jackson takes 6 hours to clean the garage by himself if he works with Mary it takes 1.5 hours how long does it take Mary if she does it by herself
whpalmer4
  • whpalmer4
Yes, that's the problem we are doing. Jackson cleans 1/6 of a garage in 1 hour of working by himself. How much of a garage does Jackson clean in 1 1/2 hours, working by himself? Once we know that, we know how much Mary can do in 1 1/2 hours working by herself, because the two amounts together add up to 1 complete garage cleaning. Understand?
whpalmer4
  • whpalmer4
I will guide you through every step of doing the problem, but you do have to do the problem yourself.
anonymous
  • anonymous
okay
anonymous
  • anonymous
i'm so confused
whpalmer4
  • whpalmer4
use your words. what is confusing you? or, what do you understand so far?
anonymous
  • anonymous
the part I understand is setting up the problem.
anonymous
  • anonymous
\[\frac{ 1 }{ 6 } =\frac{ x }{ 6}=1\] is this right so far ?
whpalmer4
  • whpalmer4
Are you familiar with the rate equation? \[x = r t\]where \(x\) is the amount done, \(r\) is the unit rate, and \(t\) is the time You can use this to calculate how far you have traveled: \[x = r t\]\[x = (30 \text{ miles}/\text{hour})*(2 \text{ hours}) = 60 \text{ miles}\]
anonymous
  • anonymous
so would 6 be at the top of the equation as x since it is the hour stated
whpalmer4
  • whpalmer4
Problems you can solve in an hour: \[x = rt\]\[r = \frac{x}{t}\]\[r = \frac{24\text{ problems}}{3 \text{ hours}} = 8 \frac{\text{problems}}{\text{hour}}\]
whpalmer4
  • whpalmer4
Let's nail down the concept first, then worry about this problem.
anonymous
  • anonymous
okay
anonymous
  • anonymous
\[\frac{ 6 }{ 1.5 }\] would the first one look something like that
whpalmer4
  • whpalmer4
sorry, got called away from my computer. Jackson does 1 garage cleaning in 6 hours. His rate is 1 garage / 6 hours, or 1/6 garage/hour
whpalmer4
  • whpalmer4
If he does 1/6 of a garage in 1 hour, how much does he do in 1.5 hours? This is probably easiest done as a fraction:\[1.5 = \frac{3}{2}\] Amount done in 1.5 hours = \[\frac{3}{2}\text{ hours} * \frac{1}{6} \frac{\text{garages}}{\text{hour}} = \frac{3}{12}\text{ garage} = \frac{1}{4}\text{ garage}\]
whpalmer4
  • whpalmer4
But Jackson and Mary working together for 1.5 hours managed to clean 1 entire garage. Jackson's cleaning + Mary's cleaning = 1 garage cleaning Jackson's cleaning = 1/4 garage cleaning 1/4 garage cleaning + Mary's cleaning = 1 garage cleaning How much of a garage does Mary clean in that time?

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