Algebra 2 word problem, only need an answer

Question

It would take Joshua 50 minutes to do the 10 questions on a team math contest. It would take Elaine 40 minutes to do the same 10 questions.  Ted would spend 30 minutes. If they all work together on the 10 questions, and they are allowed 15 minutes for the contest, home many minutes do they have left over to check their answers?

Answer 1

It's not a straight forward question.

Josh solves 1/5 q/min

Elaine solves 1/4 q/min

Ted solves 1/3 q/min

 

Add them up and you get 47/60 q/min.

 

10/(47/60) = 600/47 or 12.77 minutes leaving 2.33 minutes for checking.

 

But you can't realistically maintain efficiency with multiple people working on the same problem, which is required to use that number.

 

Josh could finish 2 at 10 minutes or 3 at 15 minutes.

Elaine could finish 3 at 12 minutes.

Ted could finish 4 at 12 minutes or 5 at 15 minutes.

 

No matter which way you split it, two of them will have some time for checking and the third person none.

Under no conditions does the tenth problem get checked.