It takes Eva 3 hours longer to do the monthly payroll than it takes Cicely. They start working on it together at 9:00 am and at 5:00 pm they have 90% of it done. If Eva took a 2 hour lunch break while Cicely had none, then how much longer will it take for them to finish the payroll working together?

Hi, first draw a timeline starting from 9 and mark the times 12, 14 hrs, 17 hrs and T, where T is the hour they finish the payroll.

Let Cicely take x hours to do payroll on her own, then she would process at a rate of (100/x) % of data per hour.

Eva takes three hours that would give a rate of 100/(x+3) %data/hour

Mark on the timeline the times when they are both working and the times when Cicely is working alone.

You'll notice that Cicely is working 8 hours and Eva only 6 hours till 17:00. Compute for each time interval the % of data or payroll that they each complete until 17:00 and equate this to 90%. Solve a quadratic in x

the quadratic is 9x^2 - 113x - 240 = 0, then for the time duration for the final 10% of work the answer is about 47 minutes.