Question

PLEASE HELP

7. SHOW YOUR WORK: Amy's Group can build 1 garage in 8 hours. Bob's
group can build it in 12 hours. How long would it take them if they worked
together? ROUND to the nearest tenth. *

Answer 1

It would take 4.8 hours if they worked together

Explanation:

The garage can be built by Amy's group in 8 hours and can be built by Bob's group in 12 hours.

Let's find what portion of the garage each group completes in one hour, add their contributions, and find the time to finish the garage working together.

Amy's group completes the job in 8 hours, it means that in 1 hour, they complete 1/8 of the garage.

Bob's group completes the job in 12 hours, meaning they complete 1/12 of the garage in 1 hour.

Now we add both contributions per hour:

`\displaystyle (1)/(8)+(1)/(12)`

The LCM of 12 and 8 is 24, thus:

`\displaystyle (1)/(8)+(1)/(12)=(3+2)/(24)=(5)/(24)`

In one hour, they build 5/24 parts of the garage, so the complete job is finished in 24/5=4.8 hours.

It would take 4.8 hours if they worked together