Question

Yesterday it took 5 cleaners 4 and 1/2 hours to clean all the rooms in a hotel. There are only 3 cleaners to clean all the rooms in the hotel today. Each cleaner is paid £8.20 for each hour or part of an hour they work. How much will each cleaner be paid today?

Answer 1

£61.50

Explanation:

Yesterday it took 5 cleaners 4 and 1/2 hours to clean all the rooms in a hotel. Then it will take
`4(1)/(2)\cdot 5=(9)/(2)\cdot 5=(45)/(2)` hours to one cleaner to clean all the rooms (5 times longer for one cleaner than for 5 cleaners).

If one cleaner cleans all the rooms in
`(45)/(2)` hours, then 3 cleaners clean all these rooms in
`(45)/(2):3=(15)/(2)` hours.

If each cleaner works today
`(15)/(2)` hours and is paid £8.20 for each hour, then each cleaner will be paid

`(15)/(2)\cdot 8.20=15\cdot 4.10=\£61.50.`