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. 
