SOLUTION: Working alone,it takes Sumalee 15 minutes to sweep a porch. Cody can sweep the same porch in 10 minutes. If they worked together how long would it take them? (Round your answer to
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Question 1122786: Working alone,it takes Sumalee 15 minutes to sweep a porch. Cody can sweep the same porch in 10 minutes. If they worked together how long would it take them? (Round your answer to the nearest hundredth) Thanks! Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
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
Sumalee makes of the job per minute.
Cody makes of the job per minute.
Working together, they make + = = = of the job per minute.
Hence, it will take 6 minutes for both to complete the job working together.
