QuestionTwo maids clean a house in 6 hours and 2 hours. How long together? A. $\frac{1}{8} \mathrm{hr}$ B. $3 \mathrm{hr}$ C. $\frac{1}{12} \mathrm{hr}$ D. $\frac{3}{2} \mathrm{hr}$

Studdy Solution

STEP 1

Assumptions1. The first maid can clean the house in6 hours. . The second maid can clean the house in hours.
3. Both maids are working together at the same time.
4. The work rate of each maid is constant.

STEP 2

We need to find the rate at which each maid works. The rate is defined as work done per unit time. In this case, since each maid can complete1 job (cleaning the house) in a certain amount of time, the rate is1 divided by the time taken.
For the first maid $Rate_{1} = \frac{1}{Time_{1}}$ For the second maid $Rate_{2} = \frac{1}{Time_{2}}$

STEP 3

Now, plug in the given values for the time taken by each maid to calculate their rates.
For the first maid $Rate_{1} = \frac{1}{6\, hours}$ For the second maid $Rate_{2} = \frac{1}{2\, hours}$

STEP 4

When both maids are working together, their rates add up. So, the combined rate is the sum of the individual rates.
$Rate_{combined} = Rate_{1} + Rate_{2}$

STEP 5

Plug in the values for the rates of the two maids to calculate the combined rate.
$Rate_{combined} = \frac{1}{} + \frac{1}{2}$

STEP 6

Calculate the combined rate.
$Rate_{combined} = \frac{1}{6} + \frac{1}{2} = \frac{4}{6} = \frac{2}{3}$

STEP 7

The time taken by both maids working together is the reciprocal of the combined rate.
$Time_{combined} = \frac{1}{Rate_{combined}}$

STEP 8

Plug in the value for the combined rate to calculate the combined time.
$Time_{combined} = \frac{1}{\frac{2}{3}}$

STEP 9

Calculate the combined time.
$Time_{combined} = \frac{}{\frac{2}{3}} = \frac{3}{2} \, hours$ So, it will take them $\frac{3}{2}$ hours to do the job working together. The correct answer is D. $\frac{3}{2} \, hours$ .

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QuestionTwo maids clean a house in 6 hours and 2 hours. How long together? A. $\frac{1}{8} \mathrm{hr}$ B. $3 \mathrm{hr}$ C. $\frac{1}{12} \mathrm{hr}$ D. $\frac{3}{2} \mathrm{hr}$

Studdy Solution

STEP 1

Assumptions1. The first maid can clean the house in6 hours. . The second maid can clean the house in hours.
3. Both maids are working together at the same time.
4. The work rate of each maid is constant.

STEP 2

STEP 3

Now, plug in the given values for the time taken by each maid to calculate their rates.
For the first maid $Rate_{1} = \frac{1}{6\, hours}$ For the second maid $Rate_{2} = \frac{1}{2\, hours}$

STEP 4

When both maids are working together, their rates add up. So, the combined rate is the sum of the individual rates.
$Rate_{combined} = Rate_{1} + Rate_{2}$

STEP 5

Plug in the values for the rates of the two maids to calculate the combined rate.
$Rate_{combined} = \frac{1}{} + \frac{1}{2}$

STEP 6

Calculate the combined rate.
$Rate_{combined} = \frac{1}{6} + \frac{1}{2} = \frac{4}{6} = \frac{2}{3}$

STEP 7

The time taken by both maids working together is the reciprocal of the combined rate.
$Time_{combined} = \frac{1}{Rate_{combined}}$

STEP 8

Plug in the value for the combined rate to calculate the combined time.
$Time_{combined} = \frac{1}{\frac{2}{3}}$

STEP 9

Calculate the combined time.
$Time_{combined} = \frac{}{\frac{2}{3}} = \frac{3}{2} \, hours$ So, it will take them $\frac{3}{2}$ hours to do the job working together. The correct answer is D. $\frac{3}{2} \, hours$ .

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QuestionTwo maids clean a house in 6 hours and 2 hours. How long together? A. 18hr\frac{1}{8} \mathrm{hr}81​hr B. 3hr3 \mathrm{hr}3hr C. 112hr\frac{1}{12} \mathrm{hr}121​hr D. 32hr\frac{3}{2} \mathrm{hr}23​hr

Studdy Solution

STEP 1

Assumptions1. The first maid can clean the house in6 hours. . The second maid can clean the house in hours.3. Both maids are working together at the same time.4. The work rate of each maid is constant.

STEP 2

STEP 3

Now, plug in the given values for the time taken by each maid to calculate their rates.For the first maidRate1=16 hoursRate_{1} = \frac{1}{6\, hours}Rate1​=6hours1​For the second maidRate2=12 hoursRate_{2} = \frac{1}{2\, hours}Rate2​=2hours1​

STEP 4

When both maids are working together, their rates add up. So, the combined rate is the sum of the individual rates.Ratecombined=Rate1+Rate2Rate_{combined} = Rate_{1} + Rate_{2}Ratecombined​=Rate1​+Rate2​

STEP 5

Plug in the values for the rates of the two maids to calculate the combined rate.Ratecombined=1+12Rate_{combined} = \frac{1}{} + \frac{1}{2}Ratecombined​=1​+21​

STEP 6

Calculate the combined rate.Ratecombined=16+12=46=23Rate_{combined} = \frac{1}{6} + \frac{1}{2} = \frac{4}{6} = \frac{2}{3}Ratecombined​=61​+21​=64​=32​

STEP 7

The time taken by both maids working together is the reciprocal of the combined rate.Timecombined=1RatecombinedTime_{combined} = \frac{1}{Rate_{combined}}Timecombined​=Ratecombined​1​

STEP 8

Plug in the value for the combined rate to calculate the combined time.Timecombined=123Time_{combined} = \frac{1}{\frac{2}{3}}Timecombined​=32​1​

STEP 9

Calculate the combined time.Timecombined=23=32 hoursTime_{combined} = \frac{}{\frac{2}{3}} = \frac{3}{2} \, hoursTimecombined​=32​​=23​hoursSo, it will take them 32\frac{3}{2}23​ hours to do the job working together. The correct answer is D. 32 hours\frac{3}{2} \, hours23​hours.

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QuestionTwo maids clean a house in 6 hours and 2 hours. How long together? A. $\frac{1}{8} \mathrm{hr}$ B. $3 \mathrm{hr}$ C. $\frac{1}{12} \mathrm{hr}$ D. $\frac{3}{2} \mathrm{hr}$

Assumptions1. The first maid can clean the house in6 hours. . The second maid can clean the house in hours.
3. Both maids are working together at the same time.
4. The work rate of each maid is constant.

Now, plug in the given values for the time taken by each maid to calculate their rates.
For the first maid $Rate_{1} = \frac{1}{6\, hours}$ For the second maid $Rate_{2} = \frac{1}{2\, hours}$

When both maids are working together, their rates add up. So, the combined rate is the sum of the individual rates.
$Rate_{combined} = Rate_{1} + Rate_{2}$

Plug in the values for the rates of the two maids to calculate the combined rate.
$Rate_{combined} = \frac{1}{} + \frac{1}{2}$

Calculate the combined rate.
$Rate_{combined} = \frac{1}{6} + \frac{1}{2} = \frac{4}{6} = \frac{2}{3}$

The time taken by both maids working together is the reciprocal of the combined rate.
$Time_{combined} = \frac{1}{Rate_{combined}}$

Plug in the value for the combined rate to calculate the combined time.
$Time_{combined} = \frac{1}{\frac{2}{3}}$

Calculate the combined time.
$Time_{combined} = \frac{}{\frac{2}{3}} = \frac{3}{2} \, hours$ So, it will take them $\frac{3}{2}$ hours to do the job working together. The correct answer is D. $\frac{3}{2} \, hours$ .