HELP PLEASE!!!

Question

If Taylor does a job in 132 hours and with the help of Michelle they can do it together in 33 hours, how long would it take Michelle to do it alone?

 

____ Hours

Answer 1

T = Taylor's rate = 1/132 jobs per hour

M = Michelle's rate = ?

 

The trick is to add their rates of work, and figuring out how to use that.

 

Jobs completed in time t is 

J = (rate)*t

 

For Taylor alone, the rate is 1/132 and the time is 132.
1 = (1/132)(132)  This is true!

 

For both of them together, the combined rate is T+M, or (1/132 + M), and time t=33.

1 = (1/132 + M)(33)

1 = 33/132 +33M

99/132 = 33M

divide both sides by 33

3/132 = M

M = 1/44  jobs per hour.

 

It would take Michelle 44 hours to complete the job alone.

 

Check:

1 =? (1/132 + 3/132)(33)

1 =? (4/132)(33)

1 =? (1/33)(33)

1 = 1    true!