Question

The contractor in charge of organizing your pool complex project has informed you that he has found two landscape companies willing to do the work. The 1st company says they can get the entire job done in 72 hours. The 2nd company says they can get the job done in 24 hours. You've decided that it would be best if both companies worked together to get the job done quicker! How many hours would it take to complete the landscaping job if the two companies worked together?

Answer 1

18 hours

Explanation:

Time taken to complete the job by 1st company =
`72\ \text{hours}`

Time taken to complete the job by 2nd company =
`24\ \text{hours}`

The job completed in 1 hour by 1st company =
`(1)/(72)\ \text{job}`

The job completed in 1 hour by 2nd company =
`(1)/(24)\ \text{job}`

The amount of job completed in 1 hour if they both work together
`1\ \text{hour}=(1)/(72)+(1)/(24)=(1)/(18)\ \text{job}\\\Rightarrow 1\ \text{job}=(18)/(1)\ \text{hours}=18\ \text{hours}`

So, if both companies work together it will take 18 hours to finish the job.