BTGmoderatorDC wrote: ↑Sat Jul 04, 2020 5:45 pm
Three hoses work to fill a tub at at different rate. Hose A and B, working together, can fill the tub in 6/5 of an hour. Hoses A and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
A. 3/10
B. 2/5
C. 1/2
D. 1
E. 6/5
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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.
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Let’s use the above rules to solve the question. . . .
Hoses A and B, working together, can fill the tub in 6/5 of an hour
Applying Rule #1, we can conclude that A and B COMBINED can fill 1/(6/5) of the tub in ONE hour
In other words, the combined rate of A and B =
5/6 tubs
per HOUR
Hoses A and C can fill it in 3/2 an hour
Applying Rule #1, we can conclude that A and B COMBINED can fill 1/(3/2) of the tub in ONE hour
In other words, the combined rate of A and C =
2/3 tubs
per HOUR
Hoses B and C can fill it in 2 hours.
So, the combined rate of B and C =
1/2 tubs
per HOUR
Let A, B, C be the RATES for each hose.
So, we can write:
A + B =
5/6
A + C =
2/3
B + C =
1/2
Add ALL three equations to get:
2A + 2B + 2C =
5/6 +
2/3 +
1/2
=
5/6 +
4/6 +
3/6
=
12/6
=
2
This means that, the COMBINED rate of all 6 (2 A's, 2 B's and 2 C's) hoses is
2 tubs PER HOUR
This means that, the COMBINED rate of 1 A, 1 B and 1 C is
1 tub PER HOUR
So if all three pools work together they can fill the tub in one hour
Answer: D
Cheers.
Brent
