Mo2men wrote:Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2

Let the job = the LCM of 10, 4 and 5 = 20 widgets.

Since A takes 10 hours to produce 20 widgets, A's rate = w/t = 20/10 = 2 widgets per hour.
Since B takes 4 hours to produce 20 widgets, B's rate = w/t = 20/4 = 5 widgets per hour.
Since C takes 5 hours to produce 20 widgets, C's rate = w/t = 20/5 = 4 widgets per hour.
Combined rate for A+B+C = 2+5+4 = 11 widgets per hour.

After A, B and C work together for an hour to produce 11 widgets, the remaining work = 20-11 = 9 widgets.
Since C's rate = 4 widgets per hour, the time for C to produce the remaining 9 widgets = w/r = 9/4 hours.

The correct answer is B.

these problems can be solved using this equation.

Job/hour * hours = job

a does .1 jobs per hour. B does .25, and c does .2

together in one hour they do .55 of the job. So .45 of the job is left

.45 is = to .05 (9) or (1/20)(9)

Since C takes 5 hours to complete the job he takes 5/20 or 1/4 of an hour to complete 1/20 the job. To complete 9/20 the job he needs to take 9/4 hours.

or we can set up a ratio. 1 job/5 hours = (9/20) jobs / x hours

5*(9/20)= 45/20=(9/4) hours

You can also be sort of "cheap" and reason that since, he takes 5 hours to do the job, doing half the job will take him 2.5 hours. He has slightly less than half the job to do and only 9/4 hours matches that.

The key to work problems imo is to understand the equation

job/hour * hours = job

The second key is to understand that you can add job/hour for multiple people.

If one person does 1/5 of the job per hour and another does 1/4 of the job per hour, then together they do the sum of that together per hour. Making a table can help especially if you are first getting started on these types of problems.