Bunuel wrote:
Official Solution:
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, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?
A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8
Break down the problem into two pieces: typing and editing.
"Mary needs 30 hours to type the report": Mary's typing rate \(= \frac{1}{30}\) job/hour;
"Mary and Jim can type up a report in 12.5": \(\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}\), where \(x\) is the time needed for Jim to type the report alone. Solving gives \(x=\frac{150}{7}\);
"Jim needs 12 hours to edit the report": Jim's editing rate \(= \frac{1}{12}\) job/hour;
"Mary and Jim can edit a report in 7.5": \(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\), where \(y\) is the time needed for Mary to edit the report alone. Solving gives \(y=20\);
"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": \(x+y= \frac{150}{7}+20 \approx 41.4\)
Answer: A
My approach is the same except that in the end, i calculate the combined Rate for Mary and Jim after having found their new rates of editing and typing respectively.
So that in the end, the time taken would be the reciprocal of the Total Rate. But then with this approach my answer changes.
Please tell me what am i doing wrong here?