Question

A machine finishes producing a coffee cup every 225 minutes and another machine finishes producing a saucer every 174 minutes. If both machines finish producing an item at 6.45PM on September 29th, then when is the next time that they finish producing an item together? Need a complete well organized solution.

Answer 1

It is given that there are 2 machines, one produces coffee cup

and other one produces a saucer.

Time taken to produce a coffee cup = 225 minutes

Time taken to produce a saucer = 174 minutes

We have to find the next time at which both the machines finish producing at the same time.

i.e. we have to find a common number which can be divided by both 225 and 174.

In other words, we need to find LCM (Least Common Multiple) of the numbers 225 and 174.

225 = 3 $\times$  75

174 = 3 $\times$ 58

LCM of 225 and 174 = 3 $\times$ 75 $\times$ 58 = 13050.

It means, both the machines will finish production together after 13050 minutes.

Converting 13050 in days and hours.

Conversion in hours, divide by 60:

$\dfrac{13050}{60} = 217\ hrs\ 30\ min$

30 minutes = 0.5 hours

Conversion to days, divide by 24:

$\dfrac{217}{24} = 9\ days\ 1\ hr$

So, 13050 minutes = 9 days 1.5 hours

So, next time when they finish production together after 29th September:

29 Sept + 9 days and 1.5 hours:

$\Rightarrow$ 8th October 08:15 PM

Answer 2

Step-by-step explanation:

It is given that there are 2 machines, one produces coffee cup

and other one produces a saucer.

Time taken to produce a coffee cup = 225 minutes

Time taken to produce a saucer = 174 minutes

We have to find the next time at which both the machines finish producing at the same time.

i.e. we have to find a common number which can be divided by both 225 and 174.

In other words, we need to find LCM (Least Common Multiple) of the numbers 225 and 174.

225 = 3 \times× 75

174 = 3 \times× 58

LCM of 225 and 174 = 3 \times× 75 \times× 58 = 13050.

It means, both the machines will finish production together after 13050 minutes.

Converting 13050 in days and hours.

Conversion in hours, divide by 60:

217\ hrs\ 30\ min

60

13050

=217 hrs 30 min

30 minutes = 0.5 hours

Conversion to days, divide by 9\ days\ 1\ hr

24

217

=9 days 1 hr

So, 13050 minutes = 9 days 1.5 hours

So, next time when they finish production together after 29th September:

29 Sept + 9 days and 1.5 hours:

8th October 8.15

hope it helps you