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A certain hotel has 1,400 single rooms and 420 double rooms. Each room

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A certain hotel has 1,400 single rooms and 420 double rooms. Each room [#permalink]

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New post 11 Nov 2015, 00:49
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A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

(A) 65
(B) 70
(C) 80
(D) 90
(E) 265

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Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room [#permalink]

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New post 11 Nov 2015, 01:13
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Number of single rooms= 1400
Number of double rooms = 420
Time taken by a person to clean a single room = 15 mins = 1/4 hour
Time taken by a person to clean a double room = 20 mins =1/3 hour

Total time to clean 1400 single and 420 double rooms
= 1400*1/4 + 420 * 1/3
= 350 + 140
= 490 hours

Each person works for = 7 hours

Number of persons required = 490/7 = 70

Answer B
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Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room [#permalink]

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New post 21 Jan 2017, 22:25
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Bunuel wrote:
A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

(A) 65
(B) 70
(C) 80
(D) 90
(E) 265


for single room, one person can clean 4 rooms in 1 hr.
thus in 7 hrs =7*4=28 rooms
Persons required for 1400 rooms= 1400/28= 50 persons
similarly
for double room, one person can clean 3 rooms in 1 hr.
thus in 7 hrs =7*3=21 rooms
Persons required for 420 rooms= 420/21 =20 persons

thus total no. of persons = persons required for single room + persons required for double rooms
=50 + 20=70

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Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room [#permalink]

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New post 03 Feb 2018, 17:41
Bunuel wrote:
A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

(A) 65
(B) 70
(C) 80
(D) 90
(E) 265

Attachment:
cleanersRTW.png
cleanersRTW.png [ 18.36 KiB | Viewed 670 times ]

1) Use a modified RT = W formula.
Add (# of workers) to LHS:
(# of workers) * rate * time = Work
Manipulate it just as you would RT = W

2) change cleaning rates from minutes to hours
(All units must be the same. Each cleaner works 7 hours.)

Single room cleaning rate in hours:
\(\frac{1room}{15mins}=\frac{4rooms}{60mins}=\frac{4rooms}{1hour}= 4\)

Double room cleaning rate in hours:
\(\frac{1room}{20mins}=\frac{3rooms}{60mins}=\frac{3rooms}{1hour}= 3\)

3) Calculate number of persons needed for each kind of room

Single rooms
\(\frac{W}{r*t}=\) number of cleaning persons needed

\(\frac{1,400}{(4*7)}=\frac{1,400}{28}= 50\) persons needed

Double rooms
\(\frac{W}{r*t}=\) number of cleaning persons needed

\(\frac{420}{(3*7)}=\frac{420}{21}= 20\) persons needed

Total persons needed: (50 + 20) = 70

Answer B
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Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room [#permalink]

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New post 17 Mar 2018, 11:47
Hi All,

This is essentially a rate question. Here's how to solve it:

Single rooms take one person 15 minutes to clean and double rooms take one person 20 minutes to clean.

15 mins. = 1/4 hour
20 mins. = 1/3 hour

With 1400 single rooms x 1/4 hour = 350 hours of total work for 1 person
With 420 double rooms x 1/3 hour = 140 hours of total work for 1 person

For ALL the rooms, we have a total of 350 + 140 = 490 hours of total work for 1 person

To get the work done in 7 hours, we'll need 490/7 = 70 workers

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Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room   [#permalink] 17 Mar 2018, 11:47
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