SOLUTION: Hi bob takes 4 hours to clean a room. Alan takes 2 hours. If bob started at 3pm and alan at 4pm what time did they finish. thanks

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Question 1148629: Hi
bob takes 4 hours to clean a room. Alan takes 2 hours. If bob started at 3pm and alan at 4pm what time did they finish.
thanks
Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Working together the whole time, the number of hours it would take them to do the job together is

%284%2A2%29%2F%284%2B2%29+=+8%2F6+=+4%2F3

Bob takes 4 hours alone to clean the room. He works 1 hour before Alan joins him, so he has done 1/4 of the job; 3/4 of the job remains to be done.

It takes them 4/3 hours to do the whole job together; the number of hours it takes them to do the remaining 3/4 of the job is

%283%2F4%29%2A%284%2F3%29+=+1

Since it was 4pm when they started working together, it will be 5pm when they finish.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, variable time hours
RATES 1/4 for bob, 1/2 for alan

%281%2F4%29%2A1%2B%281%2F4%2B1%2F2%29x=1
-
1%2F4%2B%281%2F4%2B1%2F2%29x=1
1%2B%281%2B2%29x=4
3x=3
highlight%28x=1%29
They both worked together for one hour. One hour past 4pm is 5pm.

They both finished at highlight%285pm%29.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Their combined rate of work is  1%2F2 + 1%2F4 = 3%2F4  of the job per hour.


After Bob worked 1 hour alone, he completed 1%2F4 of the job;  hence,  3%2F4  of the job remained.


With the combined rate of work of  3%2F4 jobs per hour, the two workers will complete the whole job in 1 hour.


One hour after 4 pm is 5 pm.    ANSWER

Solved.

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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.