Problem Solving

From GMAT Paper Test 37,

A certain hotel has 1,400 single 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 of the rooms if each person works for exactly 7 hours?

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

Here's how I solved the question:

x = no. of cleaning persons to work on all of the rooms

[x][(1/0.25)(7) + (1/0.33)(7)] = 1,400 + 420

x = 37.14

Clearly, I didn't answer correctly since my answer isn't in any of the choices. Can someone show me how to solve this problem? Please show and explain using the rate/time formula, so I can see where I went wrong in the equation.

I think the answer would be 70 (B).

Think of this as 2 seprate actions: cleaning the single rooms and cleaning the double rooms.

420 double rooms * (1hr/3rooms) = 140 hours of work
1400 single rooms * (1hr/4rooms) = 350 hours of work

Total hours = 490 hours of work
490 hours * (1person/7hours) = 70 people

virtualM,

Your equation suggests that each person works on both type of rooms in the same hour and this is not correct.

================
Single bedrooms = 1400*15/60 = 350 hrs
Double bedrooms = 420 * 20/60 = 140 hrs

Total time = 490hrs

1person can work 7hrs
70 people can finish the job in 490hrs.

So Answer:70 people?

Yep, the OA is B) 70.

alternate method
keep the single and double rooms separate

one person works 7 hrs or 420 minutes
that one person can clean 420/15=28 single rooms in 7 hrs and/or clean 420/20=21 double rooms in 7 hrs
if one person can clean 28 single rooms in 7 hrs then you will need 1400/28 people to clean the single rooms
and you will need 420/21 people to clean the double rooms
the sum of those two = 50+20=70