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When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 hours

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When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 hours

by Gmat_mission » Tue Nov 10, 2020 7:54 am

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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

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Re: When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 h

by deloitte247 » Thu Nov 12, 2020 8:45 pm
$$Rate=work\ done\ per\ unit\ of\ time=\frac{workdone}{time\ taken}$$
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
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Re: When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 h

by Scott@TargetTestPrep » Tue Nov 17, 2020 8:39 am
Gmat_mission wrote: ↑
Tue Nov 10, 2020 7:54 am
 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

Solution:

Mary’s rate is 1/4, and Lisa’s rate is 1/L. We can create the equation:

1/4 + 1/L = 1/3

Multiplying by 12L, we have:

3L + 12 = 4L

12 = L

Answer: D

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