Problem Solving, need help forming the equation please

• Oct 19th 2007, 07:00 AM
matholic
Problem Solving, need help forming the equation please
This is my first post so hello everyone! (Handshake)
I'm from china, my english isn't too good, please bare with me if you find my wording a bit wierd. :) I'll try my best to make myself comprehendable.

Here is the problem that gives me difficulty:
It takes Betty 2 hours longer to do a certain job than it takes Ada.They worked togeher for 3 hours then Ada left and Betty finished the job in 1 hour.How long would it take each of them to do the job alone?

I know I should let x hours be the time it takes for Ada to finish the job, then for Betty it shall be x+2 hours, however I can't figure out how to express Betty and Ada working on the same job for 3 hours in algebraic forumla, can anyone help me please?
• Oct 19th 2007, 08:03 AM
DivideBy0
These kinds of problems are definitely tricky! :D

Let the time Ada takes to do a job be x hours.
Then the time Betty takes to do the same job is x+2 hours.

$\displaystyle Work=Rate \times Time$

$\displaystyle Rate = \frac{Work}{Time}$

Therefore, Ada can do $\displaystyle \frac{1}{x}$ of the job in 1 hour.

And also, Betty can do $\displaystyle \frac{1}{x+2}$ of the job in 1 hour.

Working together they can complete $\displaystyle \frac{1}{x}+\frac{1}{x+2}$ of the job in 1 hour.

The question says, that together they work for three hours and betty works alone for 1 hour to complete the job. It follows that:

$\displaystyle 3 \left(\frac{1}{x}+\frac{1}{x+2} \right)+1\left(\frac{1}{x+2}\right)=1$

Now solve for x.
• Oct 20th 2007, 12:13 AM
matholic
Wow thanks! (Handshake) I got it now!
With the equation found , the answer is easy, 6 hours for Ada and 8 hours for Betty. :):)