A library crew can shelve books in six hours. Another crew can do the job in four hours. If the first crew begins and is joined by the second crew one hour later, how many hours will it take to finish the job?
1st crew did (1/6)job
that leaves (5/6)job to be done with combined crews.
combined rate = job/6 + job/4 = 5job/12
time to do rest of job = (5/6)job ÷ (5job/12)
= 2 hours
It will take another 2 hours to finish
To solve this problem, we can break it down into smaller steps:
Step 1: Find the combined efficiency of both crews.
First, let's find the efficiencies of both crews. The efficiency of a crew is defined as the number of books they can shelve in one hour.
The first crew can shelve books in 6 hours, so their efficiency is 1/6 of the job per hour (1 book divided by 6 hours).
The second crew can shelve books in 4 hours, so their efficiency is 1/4 of the job per hour (1 book divided by 4 hours).
To find the combined efficiency of both crews, we need to add their individual efficiencies. So:
Combined Efficiency = Efficiency of Crew 1 + Efficiency of Crew 2
Step 2: Calculate the amount of work done in the first hour.
Since the first crew starts working for one hour before the second crew joins, the first crew alone completes 1 hour * Efficiency of Crew 1 of the job.
Step 3: Calculate the remaining work.
After the first crew finishes their work in the first hour, we need to calculate the remaining work to be done. This can be calculated by subtracting the work done in the first hour from the total work.
Remaining Work = Total Work - Work Done in the First Hour
Step 4: Calculate the time it takes to finish the remaining work.
Now that we know the remaining work and the combined efficiency of both crews, we can calculate the time it takes to finish the remaining work.
Time to Finish = Remaining Work / Combined Efficiency
Let's plug in the values and solve the problem:
Efficiency of Crew 1 = 1/6
Efficiency of Crew 2 = 1/4
Work Done in the First Hour = 1 hour * Efficiency of Crew 1
Total Work = 1 (since the entire job is assumed to be 1)
Remaining Work = Total Work - Work Done in the First Hour
Remaining Work = 1 - 1/6
Time to Finish = Remaining Work / Combined Efficiency
Time to Finish = (1 - 1/6) / (1/6 + 1/4)
Calculating further:
Time to Finish = (5/6) / (10/24)
Time to Finish = (5/6) * (24/10)
Time to Finish = 5 * 24 / (6 * 10)
Time to Finish = 120 / 60
Time to Finish = 2
Therefore, it will take 2 more hours to finish the job after the second crew joins, making a total of 3 hours to finish the entire job.