At an auto detailing company, it takes 15 minutes for an

Question

At an auto detailing company, it takes 15 minutes for an employee to service a car and 24 minutes to service a truck. If the company needs to service all 300 trucks and 360 cars on a lot during a six-hour shift, how many employees will it need to complete the job?

A. 35
B. 36
C. 40
D. 42
E. 45

The OA is A.

Source: Veritas Prep

rrnicky · Answer

car servicing rate = 1/15 car per minute per employee
truck servicing rate = 1/24 truck per minute per employee
lets say n employees for car servicing and m employees for truck servicing are needed
then
cars repaired in 6 hrs (=6 x 60 min) by n employees = n x 6 x 60 x 1/15 = 360
truck repaired in 6 hrs (=6 x 60 min) by m employees = m x 6 x 60 x 1/24 = 300
solving both equations gives
n = 15, m = 20
total employees needed = 15+20 = 35

hence A is correct

Rich.C@EMPOWERgmat.com · Answer

Hi All,

We're told that at an auto detailing company, it takes 15 minutes for an employee to service a car and 24 minutes to service a truck and the company needs to service all 300 trucks and 360 cars on a lot during a 6-hour shift. We're asked for the number of employees needed to complete the job. This question can be approached in a number of different ways (depending on how you choose to organize the information).

Each car takes 15 minutes to service = 1/4 of an hour to service. With 360 cars, we would need (1/4)(360) = 360/4 = 90 hours of service to be done
Each truck takes 24 minutes to service = 2/5 of an hour to service. With 300 cars, we would need (2/5)(300) = 600/5 = 120 hours of service to be done
Total service time needed would be 90 + 120 = 210 hours of service

Since each employee is working for 6 hours, we would need 210/6 = 35 employees to complete the work in 6 hours.

Final Answer: A

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

Contact Rich at [email protected]

fskilnik@GMATH · Answer

swerve wrote:At an auto detailing company, it takes 15 minutes for an employee to service a car and 24 minutes to service a truck. If the company needs to service all 300 trucks and 360 cars on a lot during a six-hour shift, how many employees will it need to complete the job?

A. 35
B. 36
C. 40
D. 42
E. 45
Source: Veritas Prep

\[?\,\,\,\, = \,\,\,\,N\,\,\left( {{\text{for}}\,\,{\text{cars}}} \right)\,\,\, + \,\,\,M\,\,\left( {{\text{for}}\,\,{\text{trucks}}} \right)\]
Excellent opportunity for UNITS CONTROL, one of the most powerful tools of our method!

\[6\,{\text{h}}\,\,\,\left( {\frac{{60\,\min }}{{1\,{\text{h}}}}} \right)\,\, \cdot \,\,N\,{\text{employees}}\,\,\,\left( {\frac{{{\text{1}}\,{\text{car}}}}{{15\,\min \,\,\, \cdot \,\,\,1\,{\text{employee}}}}} \right)\,\,\,\, = \,\,\,\,360\,\,{\text{cars}}\,\,\,\,\, \Rightarrow \,\,\,\,\,N = 15\]
\[6\,{\text{h}}\,\,\,\left( {\frac{{60\,\min }}{{1\,{\text{h}}}}} \right)\,\, \cdot \,\,M\,{\text{employees}}\,\,\,\left( {\frac{{{\text{1}}\,{\text{truck}}}}{{24\,\min \,\,\, \cdot \,\,\,1\,{\text{employee}}}}} \right)\,\,\,\, = \,\,\,\,300\,\,{\text{trucks}}\,\,\,\,\, \Rightarrow \,\,\,\,\,M = 20\]
\[? = 15 + 20 = 35\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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