Two machines can finish a job in StartFraction 20 Over 9 EndFraction hours. Working alone, one machine would take one hour longer than the other to complete the same job. How long would it take the slower machine working alone to complete this job?

Answer

5 hours

Explanation

The two working together can finish a job in

Also, working alone, one machine would take one hour longer than the other to complete the same job.

Let the slower machine working alone take x hours. Then the faster machine takes x-1 hours to complete the same task working alone.

Their combined rate in terms of x is

This should be equal to 20/9 hours.

Multiply through by;

Factor to get:

It is not feasible for the slower machine to complete the work alone in 4/9 hours if the two will finish in 20/9 hours.

Therefore the slower finish in 5 hours.