How long would it take the faster computer, working alone, to run the program?

Question

Parallel processing is the simultaneous use of more than one computer to run a program. Suppose one computer, working alone, takes 9 h longer than a second computer to run a program. After both computers work together for 1 h, the faster computer crashes. The slower computer continues working for another 7 h before completing the program. How long would it take the faster computer, working alone, to run the program?

Answer 1

Let f and s be the number of hours it takes the faster and the slower computer, respectively, to complete the work alone. Then

 

f + 9 = s

 

For one hour the faster does 1/f of the whole work and the slower 1/s of it. Therefore, the chunks 1/f, 1/s, and 7*(1/s) add up to the whole work, i.e.,

 

1/f + 1/s + 7*(1/s) = 1

1/f + 8/s = 1  | *(s*f)

s + 8*f = s*f

 

Using the first equation, s = f + 9, we find

 

f + 9 + 8*f = (f + 9)*f

9*f + 9 = f^2 + 9*f

f^2 = 9

f = 3