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 806 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) =
70Answer B
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84% (01:52) correct 
