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Question 829334: Bart can peel a batch of 3000 lbs of apples in 12 hours with an old machine, while Mona can do the same job in 8 hrs using the new machine. If Bart starts peeling at 8am and Mona joins him at 9am then at what time will they finish the batch working together. So far I have 1/t1+1/t2=1/t3 so that is 1/12+1/8=1/x
2x+3x=24
6x=24
x=4 but I am clueless as to what I am supposed to do with the extra hour Bart has?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Let's start from here, the correct equation for their combined rate:  .
 ... but instead of solving for x, just compute the rate. That is what you really want, even if it is as a rational number, fraction form.
That is  batches per hour.
You can also say, 5 batchs in 24 hours.
Next, look at time values, not necessarily viewed on a number line. Time 8AM is time, ZERO. Let h be the time after the first hour, because Mona joins Bart after ONE hour. Bart works for 1+h hours and Mona works with him for h hours.
The total jobs done will be 1.
This one job is  ;
-
Most important is to understand the analysis, and the resulting equation. Solving it for h should be much less of a chore.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Bart can peel a batch of 3000 lbs of apples in 12 hours with an old machine, while Mona can do the same job in 8 hrs using the new machine. If Bart starts peeling at 8am and Mona joins him at 9am then at what time will they finish the batch working together. So far I have 1/t1+1/t2=1/t3 so that is 1/12+1/8=1/x
2x+3x=24
6x=24
x=4 but I am clueless as to what I am supposed to do with the extra hour Bart has?You need to realize that Bart can do the job in 12 hours, or  , of job in 1 hour
Therefore, in 1 hour (8:00 AM - 9:00 AM), he has completed of the job, which leaves  to be completed
by he and Mona.
Working together to complete the remaining work, you should get 4.4 hours, or  hours, or 4 hours, 24 minutes,
after both start (9:00 AM), which makes the end-time:  , or 
You can do the check!!
If you need a complete and detailed solution, let me know!!
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