Question 1122786
sumalee takes 15 minutes to sweep the porch.


that's 1/15 of the porch every minute.


cody can sweep the porch in 10 minutes.


that's 1/10 of the porch every minute.


for every minute, they can both sweep 1/15 + 1/10 of the porch = 2/30 + 3/30 = 5/30 of the porch.


at that rate, it will take them 6 minutes to sweep the porch because 6 * 5/30 = 30/30 = 1 swept porch.


the basic formula to use is r * t = q


r = rate
t = time
q = quantiy


q = 1 porch.


for sumalee, this formula became r * 15 = 1
solve for r to get r = 1/15.


for cody, this became r * 10 = 1
solve for r to get r = /10


when they work together, their rates are additive.


r * t = q becomes:


(1/15 + 1/10) * t = 1


combine fractions to get 5/30 * t = 1


solve for t to get t = 1 * 30/5 = 6


in 6 minutes, somalee completed 1/15 * 6 = 6/15 of the job.
in the same 6 minutes, cody completed 1/10 * 6 = 6/10 of the job.
6/15 + 6/10 = 12/30 + 18/30 = 30/30 of the job = 1