Problem Solving

When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 hours to paint a house of the same size. How long would it take for Lisa to paint a house of the same size by herself?

A. 5 hr
B. 6 hr
C. 7 hr
D. 12 hr
E. 20 hr

Answer: D

Source: Magoosh

$$Rate=work\ done\ per\ unit\ of\ time=\frac{workdone}{time\ taken}$$
Work done by Mary = painting 1 house
Time taken by Mary = 4 hours
Work done by Lisa = painting 1 house
Let the time taken by Lisa = x
Work done by both = painting 1 house
Time taken by both = 3 hours
The work done by both is as a result of their combined work rate
$$\frac{1}{4}+\frac{1}{x}=\frac{1}{3}$$
$$\frac{1}{x}=\frac{1}{3}-\frac{1}{4}$$
$$\frac{1}{x}=\frac{4-3}{12}$$
$$\frac{1}{x}=\frac{1}{12}$$
$$x=12\ hours$$
Therefore, it would take Lisa 12 hours to paint a house all by herself.

Answer = option D