linear equations

Question

It takes Al 3 hours to do a job. It takes Bob 4 and Fred 6. How fast could they do the job
together?

Answer 1

Hi Boo,

 

I bet Halloween is your favorite holiday :-)

 

To answer the question, first figure how much of the job each person does in one hour:

 

Al does 1/3 of the job in one hour and Bob does 1/4 and Fred does 1/6

 

Now add up the fractions to determine how much of the job is done in one hour:

 

1/3 + 1/4 + 1/6 = 4/12 + 3/12 + 2/12 = 9/12 = 3/4

 

So 3/4 of the job is done in one hour if they work together.

 

They have to do another 1/4 of the job which is 1/3 of 3/4 so they'll need another 1/3 of an hour or 20 minutes.

 

Total time = 1 hour 20 minutes.

 

Happy Halloween.

 

Dan

Answer 2

This is a word problem. let's write the fractional job done by each. Al=1/3, Bob =1/4, Fred= 1/6. you can see these fractions if you want as their speed of getting the job done. And question is what is their combine speed to do the job? That is 1/3 + 1/4 + 1/6= 1/X . To find X here we need to find the common denominator of the left side the equation which is 12. So the equation will be (4/4)*(1/3)+(3/3)*(1/4)+(2/2)*(1/6)=1/X ----> (4+3+2)/12= 1/X ---> 9/12=1/X or X=12/9= 4/3.

They could do the job together in 4/3 hours that's approximately 1.33 hrs =1hr20mins.