Answer to May 10, 2004 Problem of the Week

Akash, Bella, Cassie, and David are house painters.

The team of Akash, Bella, and Cassie can paint my house in 3 days; if Akash and David work as a pair it takes 6 days; the pair of Cassie and David takes 8 days, and the team of Bella, Cassie, and David can finish in 5 days.

How long would it take the whole 4-person crew to paint my house?
(Answer to the nearest minute if necessary)

Solution to the Problem:

The answer is 2 and 6/7 days, which is equivalent to 2 days, 20 hours, 34 minutes.
Let A = days Akash would take to paint the house himself,
B = days for Bella alone,
C = days for Cassie alone,
and D = days for David alone.

Then Akash can do 1/A of the house in a day.
If Akash, Bella, and Cassie take 3 days,
then the fractions for one day give : (1/A) + (1/B) + (1/C) = 1/3 ;
letting small letters a, b, c, d replace 1/A, 1/B, 1/C, 1/D :
we get the linear system
{a + b + c = 1/3 ,
a + d = 1/6 ;
c + d = 1/8 ;
b + c + d = 1/5}.

The solution is : a = 3/20 , b = 3/40 , c = 13/120 , d =1/60 ;
so that all four together would paint a + b + c + d = 7/20 of the house in a day;
it would take 20 / 7 days which is 2 and 6/7 days.
This is 2 days, 20 hours, 34 minutes and change.

James Alarie responded, "You asked for the answer to the nearest minute, but 'nearest' is ...34 minutes and the job would not be complete. I think that we had better allow them ...35 minutes."

Correctly solved by:

1. Rich Murray	Ridgetown, Ontario, Canada
2. Richard Johnson	La Jolla, California
3. Jeffrey Gaither	Winchester, Virginia
4. James Alarie	University of Michigan -- Flint Flint, Michigan
5. Julie	Dallas, Texas
6. Dave Smith	Toledo, Ohio
7. Jason Storer	Winchester, Virginia
8. David & Judy Dixon	Bennettsville, South Carolina
9. Chris Maggiolo	Harrisonburg, Virginia
10. Mikael Wetterholm	Danderyd, Sweden

May 10, 2004 Problem of the Month

Correctly solved by:

May 10, 2004
Problem of the Month