A paint manufacturing company has a machine which fills 24 tins with paint in 5 minutes.
(I) How many tins will the machine fill in?
(a) 1 minutes, correct to the nearest whole number?
(b) 1 hour?
(ii) How many hours will it take to fill 1440 tins?
(I)
(a) In one minute, the machine fills:
24 tins/5 minutes = 4.8 tins/minute
Rounding to the nearest whole number, the machine will fill approximately 5 tins in one minute.
(b) In one hour, there are 60 minutes.
The machine fills 24 tins in 5 minutes, so it will fill:
24 tins/5 minutes x 60 minutes/hour = 288 tins/hour
Therefore, the machine will fill 288 tins in one hour.
(ii) Let's use a proportion to solve for the time it takes to fill 1440 tins:
24 tins/5 minutes = 288 tins/x minutes
Cross-multiplying, we get:
24x = 5 x 288
Simplifying:
24x = 1440
x = 1440/24
x = 60
Therefore, it will take 60 minutes (or 1 hour) to fill 1440 tins.