SOLUTION: This problem is really confusing me. I've been trying for a while but just don't know how to do it. Could you help? A factory has an order for 23,500 paper clips. Machine A can

Question 1006967: This problem is really confusing me. I've been trying for a while but just don't know how to do it. Could you help?
A factory has an order for 23,500 paper clips. Machine A can make 1500 paper clips per hour while Machine B can make 2500 paper clips per hour. Machine A starts at 8:00 A.M. and Machine B starts at 1:00 P.M. At what time will the two machines complete the job?
Found 3 solutions by ptaylor, fractalier, josmiceli:
Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
OK, let t=time that both machines finish the job
Now we know that machine A and B working together makes 1500+2500=4000 clips per hour
Now machine A works alone for 5 hours(8am-1pm) before machine B starts, so Machine A makes 1500*5=7500 clips leaving 23,500-7500=16,000 clips yet to be made.
Working together, machine A and machine B can make 16,000 clips in 16,000/4000=4 hours:
Sooo t=1:00pm +4 hours=5:00pm
Hope this helps---ptaylor
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
Imagine machine A working from 8 am until 1 pm.
In those five hours, it produces 5(1500) = 7500 paper clips.
That means there are 23,500 - 7,500 = 16,000 paper clips to go.
When both machines run, they produce 1500+2500 = 4,000 paper clips an hour.
Since they have to make 16,000 more paper clips, they work together for 16,000/4,000 = 4 more hours.
They will be done at 5 pm.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
it sounds like there is 5 hrs ( 8 AM to 1 PM )
when only machine A is making paper clips
-------------------
paper clips /hr is A's rate of making them
paper cips / hr is B's rate of making them
-------------------
What part of the order does machine A get done
in 5 hrs working alone?
paper clips
----------------------------
That leaves
left to be made
-----------------
Let = the number of hrs past 1PM when both
machines working together will finish the order
-----------------
Add their rates of working to get their rate working together
Their rate working together is:
[ 16000 paper clips ] / [ t hrs ]
-----------------

( note that I am adding rates to get a rate )

hrs
------------
1 PM + 4 hrs = 5 PM when the order will be finished
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