Algebra word problem

Question

A painter can finish painting a house in 4 hours. Her assistant takes 6 hours to finish the same job. How long would it take for them to complete the job if they were working together

Answer 1

A painter paints a house in 4 hours.

She paints 1/4 of the house in 1 hour.

Her assistant paints the house in 6 hours.

Her assistant paints 1/6 of the house in 1 hour.

x=# of hours they work together.

(1/4)x+(1/6)x=1 (job finished)

multiply both sides by 12

12(1/4)x+12(1/6)x=12(1)

3x+2x=12

5x=12

x=12/5

x=2 2/5 hours or 2.4 hours working together.

 

Another way to look at this problem...

In 12 hours the painter can paint 3 houses and her assistant can paint 2 houses.

In 12 hours they can paint a total of 5 houses.

If they can paint 5 houses in 12 hours, together it takes them 12 hours/ 5 houses=2.4 hours per house.