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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?

How did I solve? Estimation approach. Advantage: fast and accurate enough Disadvantage: there is more logic than math and it won't give you the exact number. Only range

But I think that, if you are not math-genius and you can't solve that kind of problems for 2 minutes, you can try this approach.

Typing a report: Mary and Jim together: 12.5 hours. Only Mary: 30 hours Mary and Mary together: 30/2 = 15 hours. So, it means that Jim is typing faster. Jim and Jim together: less than 12.5 hours. About 12.5-(15-12.5) = 10 hours (since it is just approximation we can consider 10-11 hours). It means that Jim working alone can type a report for about 20-22 hours.

Editing a report: Mary and Jim together: 7.5 hours Only Jim: 12 hours Jim and Jim together: 12/2 = 6 hours. So, it means that Jim is editing also faster (good Jim) Mary and Mary together: more than 7.5 hours. About (7.5-6)+7.5 = 9 hours (since it is just approximation we can consider 9-10 hours) It means that Mary working alone can edit a report for about 18-20 hours.

Let's sum up. Our range is about (20+18) - (22+20) hours. Or about 38-42 hours ("-" do not read as "minus" here. It is a range).

Only A falls into this range.

Again - the official solution is much better and accurate. Use the official solution approach whenever is possible, but if you want to little bit save your time taking some risk, you can use approximation approach.