SOLUTION: Two machines can finish a a job in 20/9 hours. Working alone, one machine would take one hour longer than the other to complete the job. How long (in hours) would it take the slowe

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Two machines can finish a a job in 20/9 hours. Working alone, one machine would take one hour longer than the other to complete the job. How long (in hours) would it take the slowe      Log On


   

Question 805256: Two machines can finish a a job in 20/9 hours. Working alone, one machine would take one hour longer than the other to complete the job. How long (in hours) would it take the slower machine to finish the job?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Let h = time for fast machine to do the job by itself.
Slow machine alone, rate is 1 job in h+1 hours
Fast machine alone, rate is 1 job in h hours
Combined rate of the two machines, 1 job in 20/9 hours

1%2F%28h%2B1%29%2B1%2Fh=1%2F%2820%2F9%29
'
1%2F%28h%2B1%29%2B1%2Fh=9%2F20
20%2F%28h%2B1%29%2B20%2Fh=9
Simplest common denominator is h(h+1) so multiply both sides by this.
20h%2B20%28h%2B1%29=9%28h%5E2%2Bh%29
20h%2B20h%2B20=9h%5E2%2B9h
40h%2B20=9h%5E2%2B9h
31h%2B20=9h%5E2
9h%5E2-31h-20=0

Solution to Quadratic Equation:
highlight%28h=%2831%2Bsqrt%2831%5E2-4%2A9%2A%28-20%29%29%29%2F%282%2A9%29%29
Finish this computation for h. Use the value to find the time for the slow machine.