Hi there. I'm happy to help with this.
The BIG idea to keep in mind: when two people are working together, what you add are the rates
. You never add or subtract the times it takes to work. You add rates.
The question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?
I'm going to use the notation:
Rmt = the rate at which Mary types
Rme = the rate at which Mary edits
Rjt = the rate at which Jim types
Rje = the rate at which Jim edits
Rct = the combined typing rate
Rtt = the combined editing rate
The first two numbers tell us about combined rates.
If they type a report together in 12.5 = 25/2 hr, then their combined typing rate is Rtt = (1 report)/(25/2 hr) = 2/25.
If they edit a report together in 7.5 = 15/2 hr, then their combined editing rate is Rte = (1 report)/(15/2 hr) = 2/15.
Mary types one report in 30 hours, so Rmt = 1/30.
ADD RATES --> Rtt = Rmt + Rjt --> Rjt = Rtt - Rmt = (2/25) - (1/30) = (2/25)(6/6) - (1/30)(5/5) = 12/150 - 5/150 = 7/150
Jim's typing rate is 7/150, so he types one report in a time of 150/7 hr, approx 21 & change hours
Jim edits one report in 12 hours, so Rje = 1/12
ADD RATES --> Rte = Rme + Rje --> Rme = Rte - Rje = 2/15 - 1/12 = (2/15)(4/4) - (1/12)(5/5) = 8/60 - 5/60 = 3/60 = 1/20
Mary's editing rate is 1/20, so she edits one report in a time of 20 hr
So, the total time = (21 & change) hours for Jim to type + 20 hrs for Mary to edit = 41 and change hours
That's closest to answer choice A
I'm sorry, but I disagree with what you posted as the OA. Is it possible that you miscopied?
Does my work here make sense? Please let me know if you have any questions on what I've said here.
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