how long to finish the same job without help

Question

Tim can paint a house in 10 hours. If Alyssa helps, it takes them 4 hours. Without help, how long would it take Alyssa to finish the same job?

Answer 1

This is a shared work problem.  The formula is T/A + T/B = 1, where T= time together, A is Alyssa  alone, and B is Tim alone.  Since we are looking for Alyssa's time alone, the equation looks like this:

 

4/10 + 4/A = 1

 

Multiply by 10A (to get rid of the fractions.)

 

4A + 40 = 10A

 

Then solve for A:  A=40/6 or 6 2/3 hours.