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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?

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": \(x+y= \frac{150}{7}+20 \approx 41.4\)

Most of the work/rate problems are causing trouble to me. Is there any thread dedicated to breaking down the common types and tricks, dealing with work/rate problems.

Most of the work/rate problems are causing trouble to me. Is there any thread dedicated to breaking down the common types and tricks, dealing with work/rate problems.

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.

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?

The point is that typing and editing are two separate actions: Jim types the report and Mary edits it immediately after he is done. Hence you cannot use combined rate for those two actions.

"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 \(y=20\);

Can someone please break this out by step? I got here (as well the other step before this that is the same style of equation) during the problem but I got stuck proceeding on the math. Am I supposed to find the LCM for 7.5 and 12, add them then cross multiply? Do I just have to multiply 12 by 7.5 to quickly come up with a workable denominator?
_________________

"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 \(y=20\);

Can someone please break this out by step? I got here (as well the other step before this that is the same style of equation) during the problem but I got stuck proceeding on the math. Am I supposed to find the LCM for 7.5 and 12, add them then cross multiply? Do I just have to multiply 12 by 7.5 to quickly come up with a workable denominator?