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

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Math Expert
Joined: 02 Sep 2009
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At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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01 Mar 2017, 07:25
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Difficulty:

55% (hard)

Question Stats:

74% (02:43) correct 26% (03:07) wrong based on 192 sessions

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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

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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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01 Mar 2017, 08:26
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Bunuel 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

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

300 trucks require 300*24 minutes = 7200 mins = 120 hours i.e. 120/6 = 20 employees
360 cars require 360*24 minutes = 5400 mins = 90 Hours i.e. 90/6 = 15 employees

Total Employees required = 20+15 = 35

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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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01 Mar 2017, 08:33
Bunuel 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

1 person takes 15 minutes for 1 car
thus in 1 minute it takes 1/15 car
So in 360 minutes(6 hrs shift) he can do 360/15 = 24 cars
thus 1 person in 6 hrs can do 24 cars
total number of person required for 360 cars = 360/24 = 15 employees
Similarly
1 person takes 24 minutes for 1 truck
thus in 1 minute it takes 1/24 truck
So in 360 minutes(6 hrs shift) he can do 360/24 = 15 trucks
thus 1 person in 6 hrs can do 15 trucks
total number of person required for 300 cars = 300/15 = 20 employees

thus total employees = 15+20=35 employees

Ans A
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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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01 Mar 2017, 11:33
Bunuel 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

(300*2/5+360*1/4)/6=35 employees
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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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02 Mar 2017, 18:21
1
Bunuel 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

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.

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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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25 Apr 2018, 09:39
Bunuel 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

Attachment:

#rtwtable.png [ 29.05 KiB | Viewed 1065 times ]

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:
$$(15 + 20) = 35$$

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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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27 Nov 2018, 19:18
Bunuel 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

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

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.
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Re: At an auto detailing company, it takes 15 minutes for an employee to s  [#permalink]

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27 Nov 2018, 22:49
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.

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Re: At an auto detailing company, it takes 15 minutes for an employee to s   [#permalink] 27 Nov 2018, 22:49
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