Question

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

Answer 1

Working on it...

Answer 2

28.6 days

Answer 3

robtobey, please show your solution steps

Answer 4

I don't know why you solve a problem like this without doing so.

Answer 5

I am working on the solution presentation.

Answer 6

Sorry about that. 28.6 appears to be incorrect. 18 days seems to be the answer.
Any one else willing to confirm or deny?

Refer to the attached Mathematica solution.

Answer 7

What does 1/a mean?

Answer 8

Right now, it doesn't mean anything to me

Answer 9

@robtobe, wouldn't this be right
a=30-b (as a+b=30)
c=24-b (as b+c=24)
the third equation is c+a=20
substituting c as 24-b and a as 30-b we get B=17

Answer 10

the above is just to get the start days

Answer 11

Hero,
1/a represents the time it takes for A to do the job alone.

Answer 12

What does A mean?

Answer 13

or a rather

Answer 14

Worker "A" from the problem's first sentence.

Answer 15

Andrew, Ben and Casey

Answer 16

Labeling workers A, B, and C are like labeling objects. I don't understand objects. I only understand people

Answer 17

I guess that the idea of manipulating symbols like Albert, Barbara, Charles becomes unwieldy to deal with over time, especially if one has to write out the lengthy variable names with pen and paper while solving this and that.

Answer 18

I was just saying I'd rather think of people in terms of their names rather than as workers

Answer 19

Its an intuitive thing. When I am describing a solution, I'd rather be describing how many hours it took for Andrew to complete the job rather than how many hours it took worker A to complete the job. A, B, and C can still be the variables

Answer 20

I think it would be great for your own solutions if you assigned full names to variables. One is not absolutely required to use the symbols x, y, z, u and so on for naming variables.

Answer 21

Gota go. Thanks for the comments. Been interesting.