The third team member takes 54 minutes to complete a report. This was determined by calculating the total reports completed by Mary and Matt in 4.5 hours and dividing the remaining reports to be completed by the total time in minutes.
Calculating the Time Required for the Third Team Member
To solve for how long it takes the third team member to complete a report, we first need to determine how many reports Mary and Matt can complete in 4.5 hours. Mary completes a report in 30 minutes, therefore, in 4.5 hours (which is 270 minutes), she can complete 270 / 30 = 9 reports. Matt completes a report in 45 minutes, hence in 4.5 hours, he can complete 270 / 45 = 6 reports. Together, Mary and Matt can complete 15 reports (9 + 6), leaving 5 reports (20 - 15) for the third team member. Since the total time spent by the team is 4.5 hours, and all 20 reports are done in this time, we can deduce the time the third member would take for one report by dividing the total time by the number of reports they complete: (4.5 hours * 60 minutes/hour) / 5 reports = 54 minutes per report. Thus, the third team member takes 54 minutes to complete a report.