A professional janitor can clean a certain high school in 8 hours, wor

Question

A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?

A. -$56
B. -$6
C. $0
D. $6
E. $8

A. -$56
B. -$6
C. $0
D. $6
E. $8

BrentGMATPrepNow · Accepted 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. . . .
  A professional janitor can clean a certain high school in 8 hours  
So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR

A student sentenced to detention can clean that same high school in 20 hours  
So (applying rule #1), the student can clean 1/20 of the school in ONE HOUR

So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR
1/8 + 1/20 = 5/40 + 2/40 = 7/40
So, in ONE HOUR they can clean 7/40 of the school.

Applying rule #2, it will take  them   40/7 hours  to clean the ENTIRE school.

The janitor earns $21/hour and the student earns $7/hour, so their combined rate is  $28/hour . 
Their  combined wages  = (pay rate)(time) = (  $28/hour )( 40/7 hours ) =   $160

Working ALONE, the janitor takes 8 hours and earns $21/hour
So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =  $168

$168  -   $160   = $8, so the answer is E

Cheers,
Brent

mmss · Answer

GMATPrepNow

Hi Brent.
Why shouldn't I consider the whole hour for the wage of the janitor plus the student, since they are paid hourly?

Total cost to pay the student and the janitor to do the job together would be 42/7 (in order to be an integer) *($28/hour)=$168

Thanks

BrentGMATPrepNow · Answer

There's nothing in the question to suggest that the workers must be paid in 1-hour increments. 
So, for example, if you work for 0.5 hours, then you receive half of your hourly rate.

Cheers,
Brent

mangamma · Answer

Correct Answer: (E)

Start by determining how long it will take each group to do the task. We’re told the janitor will take a flat 8 hours, so that part’s easy: the cost to pay him alone is 8 * $21 = $168. The student can do the job in 20 hours, so they perform 1/20 of the job per hour.. The janitor can perform 1/8 of the job per hour, and the student and the janitor combined can do 1/8 of the job + 1/20 of the job in one hour, or 7/40 of the job. Take the reciprocal to find the number of hours it takes the student and janitor combine to complete the entire job: 40/7 hours. Together, they are paid $28/hour. Multiply 40/7 by 28 to find a total of $160. The janitor gets paid $8 more to do the job alone.

mailson · Answer

Given:
J =  \frac{1}{8} 
S = \frac{1}{20} 
J + S =  \frac{7}{40}

To find:
  -   = ?

Approach:
 - J PMT =  8 * 21 
 - J+S PMT =  \frac{40}{7}*(21+7)

-   =  8*21 - \frac{40}{7}*(21+7) = 8 * 21 - \frac{40}{7}*28 = 8 * 21 - \frac{8*5}{1}*4

8 * 21 - 8 * 20 = 8 * 1

QuantMadeEasy · Answer

Using equation RT=W

Rate of Janitor = 1/8
Rate of Student = 1/20

Combined rate = 7/40
Time taken by both working together = 40/7
Combined cost = (40/7)*28 = 160

Cost when only Janitor does the work = 8*21 = 168

Extra amount = 8$
E is correct

TheNightKing · Answer

Official Explanation

Start by determining how long it will take each group to do the task. We’re told the janitor will take a flat 8 hours, so that part’s easy: the cost to pay him alone is 8 * $21 = $168. The student can do the job in 20 hours, so they perform 1/20 of the job per hour.. The janitor can perform 1/8 of the job per hour, and the student and the janitor combined can do 1/8 of the job + 1/20 of the job in one hour, or 7/40 of the job. Take the reciprocal to find the number of hours it takes the student and janitor combine to complete the entire job: 40/7 hours. Together, they are paid $28/hour. Multiply 40/7 by 28 to find a total of $160. The janitor gets paid $8 more to do the job alone.

ScottTargetTestPrep · Answer

If the janitor cleans the school by himself, it will cost the school 21 x 8 = $168.

The janitor’s rate is 1/8, and the student’s rate is 1/20. If we let t = the number of hours it takes if the janitor works together with the student to clean the school, we can create the equation:

(1/8 + 1/20) x t = 1

t/8 + t/20 = 1

5t + 2t = 40

7t = 40

t = 40/7

Therefore, if they work together, it will cost the school 21 x 40/7 + 7 x 40/7 = 120 + 40 = $160. We see that it will cost the school 168 - 160 = $8 more if the janitor works alone.

Answer: E

Basshead · Answer

Janitor rate = 1/8
Student rate = 1/20

Janitor + Student rate = 1/8 + 1/20 = 7/40

Janitor is paid $21 * 8 = 168 to complete the job.

How much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?

Combined, the janitor and student are paid $28 each hour.

40/7 * 28 = 160

168 - 160 = $8 more dollars

Answer is E.

bumpbot · Answer

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A professional janitor can clean a certain high school in 8 hours, wor

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