Eight workers from Company A can paint 7 homes in 84 hours. Working to

Question

Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and the amount of time required to paint each home is the same, how many workers from Company B are required to 9 paint homes in 60 hours?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

(A) 12 
(B) 13 
(C) 14 
(D) 15 
(E) 16

The 8 workers from A can paint 1/12 of a home in 1 hour. Thus each worker A can paint 1/96 of a home in 1 hour

3 from A and 5 from B can paint 9/96 of a home in 1 hour- Since the 3 A's together paint 3/96 per hour, the 5 from B paint 6/96 of a home in 1 hour, or 1/80 each per hour.

In 60 hours, x B workers paint 60x/80= 3x/4 homes
Solving 3x/4= 9 for x, we get x=4(9)/3 =12 hours

Spidy001 · Accepted Answer

8 from company A can paint 7 homes in 84 hours =>A's rate = 1/96

3 from company A and 5 from B can paint 9 homes in 96 hours

=> 3/96 + 5B = 1/(96/9)
 => B's rate = 1/80

1 person from B can paint 1/80 of the homes in an hour.

=> 1 person from B can paint (1/80)*60 = 3/4 of the homes in 60 hours

=> 3x/4 = 9 => x=12

EMPOWERgmatRichC · Answer

Hi All,

These types of layered "work" questions can sometimes be confusing to look at, but they're based on arithmetic, so you just have to be careful with your math and take good notes. Here's how to solve this problem step-by-step:

Let's break the prompt into pieces....

1) We're told that 8 workers from Company A can paint 7 homes in 84 hours. This means...

8 workers can paint 7 homes in 84 hours = 
8 workers can paint 1 home in 12 hours

So, for those 12 hours, ALL 8 workers need to paint to get the job done. This means...
1 worker from Company A would need 8(12) = 96 hours to paint 1 home by himself.

2) We're told that 3 workers from Company A and 5 from Company B can paint 9 homes in 96 hours.

We already know that 1 worker from Company A can paint an ENTIRE HOME BY HIMSELF in 96 hours. 
Those 3 workers from Company A will end up painting 3 (of the 9) homes in 96 hours.

This leaves 5 workers from Company B to paint 6 homes in 96 hours. This means...

5 workers can paint 6 homes in 96 hours = 
5 workers can paint 1 home in 16 hours

So, for those 16 hours, ALL 5 workers need to paint to get the job done. This means....
1 worker from Company B would need (5)(16) = 80 hours to paint 1 home by himself

3) Now that we know the rate for each worker from Company B, we can answer the final question:

How many workers from Company B are required to paint 9 homes in 60 hours.

This final calculation can be done as a ratio or as a rate:

1 worker paints 1 home in 80 hours
4/3 workers paint 1 home in 60 hours
9 homes in 60 hours = 9(4/3 workers) = 36/3 = 12 workers

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

PareshGmat · Answer

.................... Rate .............. Workers .............. Hours ................... Homes (Work Done)

Company A .....  \frac{1}{96}  .................. 8 ...................... 7 .......................... 1

Company B ...  \frac{1}{b}  .................... b .......................... 1 ....................... 1 (b is the assumption)

Given that 3 Company A workers & 5 Company B workers together make 9 homes in 96 hours

Setting up the equation

(\frac{1}{96} * 3 + \frac{1}{b} * 5)96 = 9

b = 80

Let w = No. of workers required of Company B to paint 9 homes in 60 hours

\frac{1}{80} * w * 60 = 9

w = 12

Answer = A

ssriva2 · Answer

Great explanation.kudos to you! :-D

Asterixspidy · Answer

This is how I approached the problem.

Stmt 1 - Eight workers from Company A can paint 7 homes in 84 hours 
=> 8/A = 7/84. 
this gives A = 96hrs. 
So 1 emp from A alone can complete 1 house in 96 hrs.

Stmt 2 - Three workers from Company A and five workers from company B can paint 9 homes in 96 hours
=> 3/A + 5/B = 9/96.
Substitute A= 96, we get 5/B = 9/96 - 3/96, gives B = 80
So 1 emp from B alone can complete 1 house in 80 hrs.

Reqd - how many workers from Company B are required to 9 paint homes in 60 hours
 => X/B = 9/60, where X is number of workers
Substitute B= 80, we get X/80 = 9/96, gives X = 12.

sananoor · Answer

1) Eight workers from Company A can paint 7 homes in 84 hours---> R*T= Work--->R= Work/time thus, 7/82=1/12-->this is the rate of 8 workers...one worker can complete one home in 12*8= 96 hours
2) Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours--->combined rates = rate of worker in A + rate of worker in B
combined rate = 9/96= 3/32
rate of worker in Company A = 1/96-->rate of 3 workers = 3*1/96 pr 1/32
thus rate of 5 workers for company B would be
3/32 = 1/32 + 5X------=3/32-1/32 = 5x-----> 1/80...therefore, One Worker in Company B can paint home in 80 hours

how many workers from Company B are required to 9 paint homes in 60 hours? 
Rate * Time = Work
1/80X * 60 = 9----->X stands for number of workers
solving above equation one will get X = 12
Thus Option A is the answer

oxy123 · Answer

very well explained sananoor

mathivanan · Answer

Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and the amount of time required to paint each home is the same, how many workers from Company B are required to 9 paint homes in 60 hours?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

(A) 12 
(B) 13 
(C) 14 
(D) 15 
(E) 16

company A
8w 7homes 84 hours
8w 1home 12 hours
1w 1home 96 hours

company A 3w 3 homes 96 hours
company B 5w 6 homes 96 hours
 5w 1 home 16 hours
 1w 1h 80 hours
 1w 9h 720 hours
 12w 9 homes 60 hours

law258 · Answer

Company A  
W =RxT --> 7 = 8R x 84 --> 7 = 672R --> 1/96 = R (rate per worker @ Company A)

Company A + Company B on a project:

(3/96)+(5W/T)=9/96 
5W/T=(6/96)
5W/T=1/16 --> W/T = 1/80

Company B 
W=RxT --> 9 = (1/80)R x 60
9=(3/4)R
36=3R
 R = 12

GyMrAT · Answer

The question utilizes the concept of Man hours of labor utilized/required.

Total Man Hours = Total Men required/employed * Total no. of hours of labor

Given, for Company A

8 workers can paint 7 homes in 84 hours.

Total Man hours required to paint 7 homes = 8 * 84 man hours

Hence for Company A Man hours required to paint 1 home or Rate of company A = (8 * 84)/7 = 96 man hours/home

Now 3 workers from Company A & 5 workers from company B can paint 9 homes in 96 hours.

Lets consider only Company A, its 3 workers work for 96 hours, hence a total of (3 * 96 ) man hours.

# of homes painted by Company A workers in (3 * 96) man hours = Total Man hours / Rate of company A = (3 * 96)/96 = 3 homes

Hence the Balance 6 homes (9 - 3) are painted by the 5 workers of Company B in 96 hours.

Therefore, for Company B Man hours required to paint 1 home or Rate of company B = (5 * 96)/6 = 80 man hours/ home

Now asked is, # of workers of Company B required to paint 9 homes in 60 hours.

Firstly total man hours required by workers of Company B to paint 9 homes = (# of homes) * ( Rate of company B per home ) = 9 * 80 =720 Man hours

Now, to finish the job in 60 hours, # of workers required = 720 / 60 = 12 workers

Answer A.

Hope it helps.

Thanks,
GyM

JeffTargetTestPrep · Answer

Case 1:

If the rate of one worker at Company A is a, then:

rate × time = work

8a × 84 = 7

a = 7/  = 1/96

Case 2:

If the rate of one worker at Company B is b, then:

rate × time = work

× 96 = 9

1/32 + 5b = 3/32

b = 1/80

Case 3:

If the number of Company B workers needed in this case is k, then:

rate × time = work

(k)(1)/80 × 60 = 9

k = 12

Answer: A

bumpbot · Answer

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