candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
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.
Now onto the question...
Sally can paint a house in 4 hours, and John can paint the same house in 6 hours
So, according to
green rule, Sally paints 1/4 of the house in
1 hour, and John paints 1/6 of the house in
1 hour
COMBINED, the fraction of the house they can paint in
1 hour = 1/4 + 1/6
= 3/12 + 2/12
= 5/12
So,
they can paint 5/12 of the house in 1 hour
If they can paint 5/12 of the house in
1 hour, then according to
blue rule, they can paint ENTIRE house in 12/5 hours.
12/5 hours = 2 2/5 hours
= 2 hours and a bit
=
A
Cheers,
Brent
