SOLUTION: A can clean a room in 5 hours. After A worked alone for 2 hours, B joined him. Together they finished cleaned the room in an hour. How long would it take B to clean the room?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can clean a room in 5 hours. After A worked alone for 2 hours, B joined him. Together they finished cleaned the room in an hour. How long would it take B to clean the room?      Log On


   

Question 980198: A can clean a room in 5 hours. After A worked alone for 2 hours, B joined him. Together they finished cleaned the room in an hour. How long would it take B to clean the room?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!

Let  x  be the time  (in hours)  it takes for  B  to cleans the room.

Then  A  is cleaning  1%2F5  of the room area in  1  hour,  and  B  is cleaning  1%2Fx  of the room area in  1  hour.  Working together,  they are cleaning  1%2F5 + 1%2Fx  of the room in  1  hour.

From the condition, you have an equation

1%2F5 + 1%2Fx = 3%2F5,

since after  2  hours  A  just cleaned  2%2F5  of the room  and only  3%2F5  remained to clean.

Solve this equation step by step:

x + 5 = 3x,     (after multiplying both sides of the equation by  5x)
2x = 5,
x = 2.5.

Answer.  It will take  21%2F2  hours for  B  to clean the room working alone.


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Oh darn it! She's already done it for you before I could post this!
To prevent students from merely turning in my answers to multiple choice
homework problems, instead of doing the exact same problems, I do a
problem EXACTLY similar to it, but changing the numbers.  So the problem
I will solve is this one. You can use it as an exact model for your problem.

A can do a job in 10 hours. After A worked alone for 2 hours, B joined him.
Together they finished the job in 3 hours. How long would it take B to do
the job alone.
Begin with this statement:

A can do a job in 10 hours. 
Therefore A's work rate is 1 job per 10 hours or 1/10 job per hour.

How long would it take B to do the job alone?
Suppose it would take B x hours to do the job alone.

Then B's work rate is 1 job per x hours or 1/x job per hour

After A worked alone for 2 hours, 
The part of the job that A did in those 2 hours is found by RATExTIME

So in those 2 hours A did (1/10)(2) = 2/10 = 1/5 of the job.

That left 1-2/5 = 5/5-1/5 = 4/5ths of the job still to be done.

B joined him. 
So then their combined rate was the sum of their rates (1/10 + 1/x).

Together they finished the job in 3 hours. 
The part of the job that they did in those 3 hours is also found by
RATExTIME, and the part they did together must equal to the remaining 
4/5 of the job.  So the equation is 

             (1/10 + 1/x)(3) = 4/5

               3(1/10 + 1/x) = 4/5

                  3/10 + 3/x = 4/5

Multiply through by LCD of 10x

                     3x + 30 = 8x

                          30 = 5x

                           6 = x

So it would take B 6 hours to do the job alone

Now use this as an exact model to solve your problem.                                

Edwin