Amy and Ben can paint my house in 6 days.
Ben and Carol can paint my house in 10 days.
Amy and Carol can paint my house in 7.5 days.

How long would it take Amy to paint my house by herself?
How long would it take Bob to paint my house by himself?
How long would it take Carol to paint my house by herself?

Solution to the Problem:

Amy can paint my house by herself in 10 days.
Ben can paint my house by himself in 15 days.
Carol can paint my house by herself in 30 days.

Let A represent the number of days that it would take Amy to paint my house by herself.
Let B represent the number of days that it would take Ben to paint my house by himself.
Let C represent the number of days that it would take Carol to paint my house by herself.
Then their respective rates would be 1/A, 1/B, and 1/C job per day, where 1 represents the entire job.

Next, set up three equations:

Since Amy and Ben can paint my house in 6 days,


Since Ben and Carol can paint my house in 10 days,


Since Amy and Carol can paint my house in 7.5 days,

You now have three equations with three unknowns.
Solve simultaneously to get the answers for A, B, and C.
You can solve the first two equations for 1/B, and then substitute to get an equation in A and C:

Now substitute for 1/C to get an equation in terms of just A.

Correctly solved by:

1. K. Sengupta Calcutta, India
2. David & Judy Dixon Bennettsville, South Carolina
3. James Alarie Flint, Michigan