Question

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

Answer 1

how many garages can Jackson train per hour?

Answer 2

finding unit rates is an easy approach to solving such problems.

Answer 3

I don't quite understand how to solve it

Answer 4

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?

Answer 5

\[\frac{1\text{ garage cleaned}}{1 \text{ hour}} = \frac{1}{6} \frac{\text{garages cleaned}}{\text{hour}}\]right?

Answer 6

sorry, that should have been 6 hours in the denominator of the left hand fraction!
\[\frac{1\text{ garage cleaned}}{6 \text{ hours}} = \frac{1}{6} \frac{\text{garages cleaned}}{\text{hour}}\]

Answer 7

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.

Answer 8

Clear so far?

Answer 9

How much of a garage does Jackson get done working on his own for 1.5 hours?

Answer 10

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

Answer 11

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?

Answer 12

I will guide you through every step of doing the problem, but you do have to do the problem yourself.

Answer 13

okay

Answer 14

i'm so confused

Answer 15

use your words. what is confusing you? or, what do you understand so far?

Answer 16

the part I understand is setting up the problem.

Answer 17

\[\frac{ 1 }{ 6 } =\frac{ x }{ 6}=1\]

is this right so far ?

Answer 18

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:

\[x = r t\]\[x = (30 \text{ miles}/\text{hour})*(2 \text{ hours}) = 60 \text{ miles}\]

Answer 19

so would 6 be at the top of the equation as x since it is the hour stated

Answer 20

Problems you can solve in an hour:

\[x = rt\]\[r = \frac{x}{t}\]\[r = \frac{24\text{ problems}}{3 \text{ hours}} = 8 \frac{\text{problems}}{\text{hour}}\]

Answer 21

Let's nail down the concept first, then worry about this problem.

Answer 22

okay

Answer 23

\[\frac{ 6 }{ 1.5 }\]

would the first one look something like that

Answer 24

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

Answer 25

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 = \[\frac{3}{2}\text{ hours} * \frac{1}{6} \frac{\text{garages}}{\text{hour}} = \frac{3}{12}\text{ garage} = \frac{1}{4}\text{ garage}\]

Answer 26

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?