If Sally can paint a house in 4 hours.....

[4ever Learning]

Hi, I'm having trouble figuring out what was the equation they used to solve the problem below? The reason I have the answer now is because I got it wrong on the test, and need help figuring out how they got that answer (2 hours and 24 minutes). Can someone please break down this problem for me.

Question: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Answer: 2 hours and 24 minutes

Thank you

Peace and Blessings

 

[royhaas]

What fraction of a house can each one paint in 1 hour?

 

[stapel]

Question: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Since you posted this to the "Arithmetic" category, clearly you haven't taken any algebra courses and your test was over pre-algebra topics. This limits the tools you can use to find your answer. Fortunately, the hint (provided in the first reply) will serve to get the job done. :wink:

If you can get a job done in two hours, how much of it do you complete in one hour?

If you can get one-half of a job done in one hour, how many hours do you need to complete the job?

If you can get a job done in three hours, how much of it do you complete in one hour?

If you can get one-third of a job done in one hour, how many hours do you need to complete the job?

Take note of the numbers you used: (2 hours)(1/2 job/hr) = 1 job; (3 hours)(1/3 job/hr) = 1 job.

Sally and John need to complete one job. How much does each do per hour? Then, combining their efforts, how much does the pair complete each hour?

Then how many hours are needed?

(Your answer will be fractional, but you can easily convert this to a mixed number, and then to "hours and minutes".)

Eliz.

 

[nycfunction]

Hi, I'm having trouble figuring out what was the equation they used to solve the problem below? The reason I have the answer now is because I got it wrong on the test, and need help figuring out how they got that answer (2 hours and 24 minutes). Can someone please break down this problem for me.

Question: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Answer: 2 hours and 24 minutes

Thank you

Peace and Blessings

This type of math question is called a WORK PROBLEM.

We can make a chart or diagram to help solve this type of problem.

I will let x = the time it will take for both of them to complete the job together.

However, you can use any letter of the alphabet.

................Total Time(in hours)............Fractional Part of job (in 1 hour)

Sally................4 hours...................................1/4
John.................6 hours...................................1/6
Together...........x hours....................................1/x


We now set up a fractional equation from the chart information:

1/4 + 1/6 = 1/x

Solve for x. What is our LCD? It is 12x. Do you see why?

We must multiply by the LCD, 12x, to clear the fractions. It is much easier working without fractions.

Now, you say the answer is 2 hours and 24 minutes, right? Are you sure?

The answer cannot be 2 hours and 24 minutes.

We have this fractional equation:

1/4 + 1/6 = 1/x

After doing the algebra, x = 2_2/5.

The mixed fraction 2_2/5, in this case, means 2 hours and 40 minutes.

If you don't believe me, replace x with 2_2/5 and equate it to 1/4 + 1/6 and you will see that I am right.

Is this clear?

 

[stapel]

...I will let x = the time it will take for both of them to complete the job together....

Actually, since this was posted to the "Arithmetic" (that is, grade-school pre-algebra math) category, we cannot assume any knowledge of variables or equations. Sorry!

Eliz.

 

[jeshuea]

Hi, I'm having trouble figuring out what was the equation they used to solve the problem below? The reason I have the answer now is because I got it wrong on the test, and need help figuring out how they got that answer (2 hours and 24 minutes). Can someone please break down this problem for me.

Question: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

Answer: 2 hours and 24 minutes

Thank you

Peace and Blessings

This type of math question is called a WORK PROBLEM.

We can make a chart or diagram to help solve this type of problem.

I will let x = the time it will take for both of them to complete the job together.

However, you can use any letter of the alphabet.

................Total Time(in hours)............Fractional Part of job (in 1 hour)

Sally................4 hours...................................1/4
John.................6 hours...................................1/6
Together...........x hours....................................1/x


We now set up a fractional equation from the chart information:

1/4 + 1/6 = 1/x

Solve for x. What is our LCD? It is 12x. Do you see why?

We must multiply by the LCD, 12x, to clear the fractions. It is much easier working without fractions.

Now, you say the answer is 2 hours and 24 minutes, right? Are you sure?

The answer cannot be 2 hours and 24 minutes.

We have this fractional equation:

1/4 + 1/6 = 1/x

After doing the algebra, x = 2_2/5.

The mixed fraction 2_2/5, in this case, means 2 hours and 40 minutes.

If you don't believe me, replace x with 2_2/5 and equate it to 1/4 + 1/6 and you will see that I am right.

Is this clear?

It would be 40 minutes if every hour was 100 minutes. But 2/5 of 1 hour is 24 minutes. because it's 2/5 of 60 not 100