Francis can paint the house by himself in 6 hours, her brother Fred

Question

Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

A. 1/36
B. 1/19
C. 1/2
D. 19/36
E. 36/19

A. 1/36
B. 1/19
C. 1/2
D. 19/36
E. 36/19

BrentGMATPrepNow · Answer

For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then  in one hour , the person can complete 1/k of the job  
 Example : If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job  
 Example : If Sam can complete 1/8 of the job  in one hour , then it will take him 8/1 hours to complete the job. 
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let’s use these rules to solve the question. . . .

Francis can paint the house by himself in 6 hours  
From Rule #1, we know that, in ONE HOUR, Francis can paint  1/6  of the house

Fred can paint the house in 4 hours  
From Rule #1, we know that, in ONE HOUR, Fred can paint  1/4  of the house

Frank can paint the house in 9 hours  
From Rule #1, we know that, in ONE HOUR, Frank can paint  1/9  of the house

If they all worked together, what fraction of the house would be painted after ONE HOUR?  
Add each person's contribution for ONE HOUR: 
 1/6  +  1/4  +  1/9  =  6/36  +  9/36  +  4/36 
= 19/36

Answer: D

mesutthefail · Answer

If we find the value that all 3 people mentioned do the job "together" in one hour, it actually is equal to the answer of the question;

hence : D

Abhishek009 · Answer

Let the total work be 36 units...

Efficiency of Francis is 6 units/hour
Efficiency of Fred is 9 units/hour
Efficiency of Frank is 4 units/hour

Combined efficiency of Francis , Fred and Frank is 19 units

So, part of house that would be painted after one hour is  \frac{19}{36}

Thus, answer must be (D)  \frac{19}{36}

jalice · Answer

House painted by Francis in an hour=1/6
House painted by Fred in an hour=1/4
House painted by Frank in an hour=1/9
House painted by Francis, Fred and Frank in an hour=1/6+1/4+1/9= 19/36 (work/hour)

(D)

itsdj · Answer

Thank you! I find this very helpful! Easy to remember & it explained the problem clearly

Francis can paint the house by himself in 6 hours, her brother Fred

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Francis can paint the house by himself in 6 hours, her brother Fred

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards