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

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): You can put this solution on YOUR website!
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

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

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.

Solved.

===================

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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