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

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Math Expert
Joined: 02 Sep 2009
Posts: 61549
At an auto detailing company, it takes 15 minutes for an employee to  [#permalink]

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20 Jan 2020, 02:30
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35% (medium)

Question Stats:

81% (02:19) correct 19% (02:28) wrong based on 31 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  [#permalink]

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20 Jan 2020, 03:39
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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
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

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

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20 Jan 2020, 04:40
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

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

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20 Jan 2020, 05:57
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

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

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20 Jan 2020, 07:12
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.
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Joined: 14 Sep 2019
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Re: At an auto detailing company, it takes 15 minutes for an employee to  [#permalink]

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20 Jan 2020, 09:57
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)
Re: At an auto detailing company, it takes 15 minutes for an employee to   [#permalink] 20 Jan 2020, 09:57
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