Jack can paint his apartment in 12 hr. His wife Cheryl requires 20 hr to do the same job. How long would it take them to complete the job if they worked together?
Jack can paint his apartment in 12 hr.
His wife Cheryl requires 20 hr to do the same job.
How long would it take them to complete the job if they worked together?
1/x = 1/12 + 1/20
1/x = 32/240
x = 15/2
It would take them 7 1/2 hours to complete the job if they worked together.
Jack can paint 1/12 apartment in 1 hour.
His wife can paint 1/20 apartment in 1 hour.
Together they can paint (1/12 + 1/20 = 32/240 = 2/15) apartment in 1 hour.
Therefore it will take them 15/2 hrs = 7 hrs 30 min to paint an apartment together.
Jack does 1/12th of the appartment in 1 hour.
Cheryl does 1/20th of the appartment in 1 hour.
So in 1 hour Jack and Cheryl do 1/12+1/20 = 2/15ths of the appartment.
So in 15 hours Jack and Cheryl can do 2 appartments, therefore the one appartment can be done in 7.5 hours.
Work = time * rate
J = 1 apt / 12 hr = 1/12
C = 1 apt / 20 hr = 1/20
1 = t * (J+C)
Solve.
Comments
Jack can paint his apartment in 12 hr.
His wife Cheryl requires 20 hr to do the same job.
How long would it take them to complete the job if they worked together?
1/x = 1/12 + 1/20
1/x = 32/240
x = 15/2
It would take them 7 1/2 hours to complete the job if they worked together.
Jack can paint 1/12 apartment in 1 hour.
His wife can paint 1/20 apartment in 1 hour.
Together they can paint (1/12 + 1/20 = 32/240 = 2/15) apartment in 1 hour.
Therefore it will take them 15/2 hrs = 7 hrs 30 min to paint an apartment together.
Jack does 1/12th of the appartment in 1 hour.
Cheryl does 1/20th of the appartment in 1 hour.
So in 1 hour Jack and Cheryl do 1/12+1/20 = 2/15ths of the appartment.
So in 15 hours Jack and Cheryl can do 2 appartments, therefore the one appartment can be done in 7.5 hours.
Work = time * rate
J = 1 apt / 12 hr = 1/12
C = 1 apt / 20 hr = 1/20
1 = t * (J+C)
Solve.