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Lisa
17 days ago
9

In three hours, Company ABC can make X ball bearings. Company DEF can make X ball bearings in 4 hours. Company GHI can make X ba

ll bearings in 6 hours. Working together, how long will it take all three companies to make X ball bearings?
Mathematics
1 answer:
AnnZ [3.8K]17 days ago
8 0

Answer:

X ball bearings can be produced in 1 hour and 20 minutes

Step-by-step explanation:

Proportions

Proportions serve as an essential method for solving various common challenges. We understand that:

Company ABC manufactures X ball bearings in 3 hours.

Company DEF produces X ball bearings in 4 hours.

Company GHI generates X ball bearings in 6 hours.

In a single hour, each company is capable of producing:

ABC: X/3 ball bearings

DEF: X/4 ball bearings

GHI: X/6 ball bearings

By collaborating, they can produce

\displaystyle \frac{X}{3}+\frac{X}{4}+\frac{X}{6}

ball bearings. Operating together

\displaystyle \frac{4X+3X+2X}{12}=\frac{9X}{12}=\frac{3X}{4}

If their output is 3/4 of a ball bearing in one hour, then it will take

\displaystyle \frac{4}{3} hours to create one complete ball bearing. This translates to 1 hour and 20 minutes.

X ball bearings can be produced in 1 hour and 20 minutes

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