The Westminster Widget Company has an old machine that can produce 50 widgets in five hours. Now they have purchased a new machine that can produce 30 widgets in two hours. Working together, how long will it take the two machines to produce 100 widgets?

Old machine: 50 widgets in 5 hours
New machine: 30 widgets in 2 hours

Old machine: 10 widgets per hour
New machine: 15 widgets per hour

Both machines: 25 widgets per hour

(100 widgets)/(25 widgets per hour) = 4 hours

Answer: It will take 4 hours.

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shubhamsinha3013 shubhamsinha3013 · Answer 2 · 2022-05-24T15:59:30+02:00

Time taken by both machines to produce 100 widgets is 4 hours.

Production rate

The weight of the finished product obtained per hour of operation is referred to as the production rate.

How to determine the production rates?

First, find an old machine that can produce per hour.

An old machine that can produce 50 widgets in five hours then, produce per hour is [tex]\frac{50}{5} = 10[/tex] widgets.

Now, find a new machine that can produce per hour.

A new machine that can produce 30 widgets in two hours then, produce per hour is [tex]\frac{30}{2} = 15[/tex] widgets.

Then, they both can produce 10+15 = 25 widgets per hour.

So, time taken for both machines to produce 100 widgets is [tex]\frac{100}{25} = 4[/tex] hours.

Hence, both machines take 4 hours to produce 100 widgets.

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