Expert: Josh - 9/20/2004

Question
Jan writes the program in 10 daya.  Bob writes it in 8 days.  WIth ted's help, the three can do it in 3 days.  How long will it take ted by himself?

Answer
Hi Lynne,

What the question is getting at is the work rate.

The concept of work (W), work rate (R) and time (t) are mathematically related by this equation,

                       W=R*t      ...[#1]

What it means is that the amount of work done (W) equals the work rate (R) multiplied by the time (t) taken to do the work.

Working individually, to complete one unit of work (W=1),

(i) Jan takes 10 days (i.e., t1=10). So, his work rate is r1=W/t1 = 1/10 units of work per day.

(ii) Bob takes 8 days (i.e., t2=8). So, his work rate is r2=W/t2=1/8 units of work per day.

(iii) Ted's work rate is unknown, so call this "r3" for the moment.

If these three people are working together, their COMBINED work rate is given by the sum of r1, r2 and r3.

The one unit of work (W=1) now takes three days to complete. So,
t_combined = 3 days,
R_combined = (r1+r2+r3).

Rearranging [#1], we have
R_combined = W / t_combined.
 r1+r2+r3 = 1/3,
       r3 = 1/3 -(r1 + r2)
substituting the values for r1 and r2, using (i) and (ii),
we get, r3 = 1/3-(1/10+1/8)
r3 = 80/240 - (24/240 + 30/240)
  = 26/240
  = 13/120 units of work per day.

So, to complete 1 unit of work, it will take Ted 1/r3 days.
Answer: Just over 9 days 5 hours and 32 minutes
(the approximate value of 1/r3 is 9.23076923)

Cheers.