Question

A paint manufacturing company has a machine which fills 24 tins with paint in 5 minutes

How many tins will the machine fill in
(a) 1 minute, correct to the nearest whole number?
(B) 1 hour?
How many hours will it take to fill 1440 tins?​

Answer 1

x = number of tins filled in 1 minutes = 5 tins

y = number of tins filled in 60 minutes = 288 tins

It will take 5 hours to fill 1440 tins

Explanation:

Number of tins filled : time taken = 24 : 5

Let

x = number of tins filled in 1 minutes

Number of tins filled : time taken = x : 1

Equate both ratios

24 : 5 = x : 1

24/5 = x/1

Cross product

24 * 1 = 5 * x

24 = 5x

x = 24/5

x = 4.8

To the nearest whole number,

x = 5

x = number of tins filled in 1 minutes = 5 tins

(B) 1 hour?

1 hour = 60 minutes

Number of tins filled : time taken = 24 : 5

Let y = number of tins filled in 60 minutes

Number of tins filled : time taken = y : 60

Equate both ratios

24 : 5 = y : 60

24/5 = y/60

Cross product

24 * 60 = 5 * y

1440 = 5y

y = 1,440/5

y = 288 tins

y = number of tins filled in 60 minutes = 288 tins

C. How many hours will it take to fill 1440 tins?​

Let

z = time taken to fill 1,440 tins

Number of tins filled : time taken = 24 : 5

Number of tins filled : time taken = 1440 : z

24 : 5 = 1440 : z

24/5 = 1440/z

24 * z = 5 * 1440

24z = 7,200

z = 7,200/24

z = 300 minutes

300 minutes = 300/60

= 5 hours

z = 5 hours

It will take 5 hours to fill 1440 tins