Question

If patricia were to paint her living room alone, it would take 4 hours. her sister naomi could do the job in 5 hours. how long would it take them working together? if needed, submit your answer as a fraction reduced to lowest terms.

Answer 1

Practicia completes the job in one hour = 1/4

Naoimi completes the job in one hour = 1/5

If Parcticia and Naoimi does it together,let us suppose in x number of hours.

The equation so form is:

(1/4)*x + (1/6)*x = 1 (i.e job finished)

The Least common multiple(LCM) of 4 and 6 = 12

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

Therefore, solving the equation we get,

3x + 2x = 12

5x = 12

x = 12/5

x= 2 2/5 hours or 2.24 hours

Therefore number of hours they took to complete the work is 2 hours and 24 minutes or 2.24 hours.