Question

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 ball bearings in 6 hours. Working together, how long will it take all three companies to make X ball bearings?

Answer 1

Answer:

X ball bearings will be made in 1 hour and 20 minutes

Step-by-step explanation:

Proportions

The proportions give us an important tool to easily solve common problems of any type. We know that:

Company ABC can make X ball bearings in 3 hours.

Company DEF can make X ball bearings in 4 hours.

Company GHI can make X ball bearings in 6 hours.

In one hour, each company can make

ABC: X/3 ball bearings

DEF: X/4 ball bearings

GHI: X/6 ball bearings

Working together, they can make

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

ball bearings. Operating

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

If they can make 3/4 of a ball bearing in one hour, then one complete ball bearing will need

$\displaystyle \frac{4}{3}$ hours to complete. It's equivalent to 1 1/3 hours or 1 hour and 20 minutes

X ball bearings will be made in 1 hour and 20 minutes