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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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11 Nov 2015, 00:49
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Difficulty:

15% (low)

Question Stats:

82% (02:35) correct 18% (03:00) wrong based on 233 sessions

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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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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

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Posts: 992
Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room  [#permalink]

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21 Jan 2017, 22:25
1
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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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 [ 18.36 KiB | Viewed 1650 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

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

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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]

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13 Mar 2019, 06:44
Top Contributor
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

The hotel has 1,400 single rooms, and one person can clean a single room every 15 minutes
So, one person can clean 4 single rooms in ONE HOUR
In other words, it takes 1 WORKER HOUR to clean 4 single rooms

1400/4 = 350
So, it takes 350 WORKER HOURS to clean 1400 rooms

The hotel has 420 double rooms, and one person can clean a double room every 20 minutes
So, one person can clean 3 double rooms in ONE HOUR
In other words, it takes 1 WORKER HOUR to clean 3 double rooms

420/3 = 140
So, it takes 140 WORKER HOURS to clean 420 double rooms

How many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?
350 + 140 = 490
So, 490 WORKER HOURS are required to clean ALL of the room.

490/7 = 70.
So, 70 workers are needed.

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

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15 Mar 2019, 06:02
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

It takes 1400 x 1/4 = 350 hours to clean the single rooms and 420 x 1/3 = 140 hours to clean the double rooms, for a total time of 490 hours. We can let n = the number of workers and create the equation:

7n = 490

n = 70

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Re: A certain hotel has 1,400 single rooms and 420 double rooms. Each room   [#permalink] 15 Mar 2019, 06:02
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