At an auto detailing company, it takes 15 minutes for an employee to s

(300*2/5+360*1/4)/6=35 employees

Since each car takes 15 minutes to service, the time to service 360 cars = 360 x 15 = 5,400 minutes.

Since each truck takes 24 minutes to service, the time to service 300 trucks = 300 x 24 = 7,200 minutes.

The total number of minutes to service these cars and trucks is 5,400 + 7,200 = 12,600 minutes or 12,600/60 = 210 hours. However, this is the required time if there is only 1 employee in the company. If there are 2 employees, the time will be cut in half, or 105 hours; if there are 3 employees, the time will be cut by 3, or 70 hours, etc. Thus, we need to find the number of employees so that the time will be cut to 6 hours. Since 210/6 = 35, we need 35 employees to cut the time to a 6-hour shift.

Answer: A

Careful . . . prompt lists "cars and trucks,"
then "trucks and cars"
We have rate in minutes, time in hours, and total W
Find rate in hours. With R, T, and W, find # of employees.

(1) Find RATE in # of vehicles/HOUR

Cars: 15 minutes each

Rate, \(R\): How many cars per hour?

\(R_{c}:\) \(\frac{1}{15min}=\frac{4}{60min}=\)
\(R_{c}:\) \(\frac{4}{1hr}\)\(=4\) cars per hour

Trucks: 24 minutes each

Rate, \(R\): How many trucks per hour?

\(R_{t}:\) \(\frac{1}{24}=\frac{2.5}{60}\)

\(=\frac{\frac{5}{2}}{60min}=\frac{\frac{5}{2}}{1hour}\)
\(R_{t}\): \(=\frac{5}{2}\) cars per hour

(2) How many employees needed to complete the job?
Use modified RT=W equation (see table)

Cars: # of workers needed to finish 360 in 6 hours?

(Number, N, of workers) * R * T = W

\(N_1 * 4 * 6 = 360\)
\(N_1 = \frac{360}{24}\)
\(N_1 = 15\)

Trucks: # of workers needed to finish 300 in 6 hours?

(N) * R * T = W

\(N_2 * \frac{5}{2} * 6 = 300\)
\(N_2 * \frac{30}{2} = 300\)
\(N_2 * 15 = 300\)
\(N_2 = 20\)

(3) Total workers/employees needed:
\((15 + 20) = 35\)

Answer A

\(?\,\,\,\, = \,\,\,\,N\,\,\left( {{\text{for}}\,\,{\text{cars}}} \right)\,\,\, + \,\,\,M\,\,\left( {{\text{for}}\,\,{\text{trucks}}} \right)\)

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.

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:

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

15 minutes for an employee to service a car
24 minutes to service a truck

300 trucks and 360 cars, during a six-hour shift

In a six hour shifts the number of cars that can be serviced by one employee = 6*60/15 = 24
i.e. for 360 cars employees needed = 360/24 = 15

In a six hour shifts the number of trucks that can be serviced by one employee = 6*60/24 = 15
i.e. for 300 trucks employees needed = 300/15 = 20

Total needed employees = 15+20 = 35

Answer: Option A

total possible cars which can be serviced in 1 hr ; 60/15 ; 4
and trucks ; 60/24 ; 2.5
total hrs ; 6 hrs
i.e total cars possible ; 4*6 ; 24 and trucks ; 6*2.5 ; 15
so for 300 trucks and 360 cars ;
300/15 ; 20
360/24 ; 15
total ; 35
IMO A

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?


Solution:
Time taken by 1 man to service a car = 15 min
Total time = 6 hours = 6 x 60 = 360 minutes
=> Number of cars that 1 man can service in 360 min = 360/15 = 24
=> Number of men required for 360 cars = 360/24 = 15 men

Time taken by 1 man to service a truck = 24 min
Total time = 6 hours = 6 x 60 = 360 minutes
=> Number of trucks that 1 man can service in 360 min = 360/24 = 15
=> Number of men required for 300 trucks = 300/15 = 20 men

Thus, total number of men = 15 + 20 = 35

Answer A



Alternate approach:
Time taken by 1 man to service a car = 15 min
Time taken by 1 man to service a truck = 24 min
Thus, we can say: 8 cars = 5 trucks (since both take 120 minutes; 120 is the LCM of 15 and 24)

Thus, 300 trucks and 360 cars = 300 * (8/5) + 360 = 840 cars
Number of cars that 1 man can service in 360 min = 360/15 = 24

=> Number of men required for 840 cars = 840/24 = 35 men

For car time = 15 min

in 6hrs = 360 min , one employee can complete 360/15 = 24 cars, for 360 cars , we need 360/24 = 15 employees

for truck=24 min , one employee can complete 360/24 = 15 trucks, for 300 trucks , we need 300/15 = 20 employees

15+20 = 35 employees in total.

Here total time needed = 6 hours = 6*60 minutes =360 minutes for cars and trucks
To service Car:
1 employee needs 15 minutes to service 1 car
1…………………360…………………….360/15 = 24 cars
24 cars are serviced by 1 employee
360…………………….360/24 = 15 employee

To service Trucks:
1 employee needs 24 minutes to service 1 truck
1…………………360…………………….360/24 = 15 trucks
15 trucks are serviced by 1 employee
300…………………….300/15 = 20 employee
Total number of employees = 15 + 20 = 35(A)

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