Mulching math problem

Question

Anita can Mulch the college gardens in 3 fewer days than it takes Tori to mulch the same areas. When they work together, it takes them 2 days. How long would it take each of them to do the job alone?

Answer 1

Suppose that n days are required by Tori to do this entire job, alone; then Anita can do it in n-3 days.

Therefore their individual rates (fraction of whole job per day) are 1/n and 1/(n-3), respectively.

The fact that they can do this in two days, together, means

2(1/n) + 2[1/(n-3)] = 1.  

THIS IS # DAYS PER PERSON TIMES PERSON'S FRACTION-OF-JOB, accumulated to do 1 entire job.

 

Solve this equation for n (and n-3).  Check the answers!