math word problem

Question

One painter can paint a house in 9 days, yet a more experienced painter can paint the house in 5 days. How many days would it take the two painters, working together, to paint the house?

 

it will take them _______ days to paint the house together

Answer 1

(1/9) + (1/5) = (1/x)

 

1/x = 14/45 and x = 45/14 = 3 3/14

 

It is always hard to explain why work problems usually look like reciprocals.  It is because the terms are rates,

e.g. the unit of 1/9 is houses per day.  Then the time worked together becomes a common factor which divides out of the equation leaving the equation as first written above.