In checking records, a contractor finds that a crew A can pave a certain lenght of highway in 9hr, while crew B can do the same job in 12 hr. How long would it take if they worked together ?
Hello, diehardmath4!
Crew A can pave a certain length of highway in 9 hours,
while crew B can do the same job in 12 hours.
How long would it take if they worked together?
Crew A can do the job in 9 hours.
. . In one hour, it can do $\displaystyle \tfrac{1}{9}$ of the job.
. . In $\displaystyle x$ hours, it can do $\displaystyle \tfrac{x}{9}$ of the job.
Crew B can do the job is 12 hours.
. . In one hour, it can do $\displaystyle \tfrac{1}{12}$ of the job.
. . In $\displaystyle x$ hours, it can do $\displaystyle \tfrac{x}{12}$ of the job.
Working together for $\displaystyle x$ hours, they can do: .$\displaystyle \tfrac{x}{9} + \tfrac{x}{12}$ of the job.
But in $\displaystyle x$ hours, we expect them to complete the job (1 job).
There is our equation: .$\displaystyle \frac{x}{9} + \frac{x}{12} \;=\;1$
Now solve for $\displaystyle x$ . . .