SOLUTION: Mandelbrot can landscape a yard in two 8-hour workdays. He can do the same job in 10 hours if he works with Descartes. If Descartes works alone, how many hours will it take him

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Mandelbrot can landscape a yard in two 8-hour workdays. He can do the same job in 10 hours if he works with Descartes. If Descartes works alone, how many hours will it take him       Log On


   

Question 925052: Mandelbrot can landscape a yard in two 8-hour workdays. He can do the same job in 10 hours if he works
with Descartes. If Descartes works alone, how many hours will it take him to landscape the yard?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
in terms of hours
rate for A alone 16
rate for A & B together 10
1/a+1/b=1/x
1/16+1/b=1/10
1/b=1/10-1/16
1/b=16/160-10/160
1/b=6/160
1/b=1/26.6666667
b=26.6666667
rate for B alone 26.6666667
check
1/16+1/26.6666667=1/10
26.6666667/426.666667+16/426.666667=1/10
42.6666667/426.666667=1/10
ok
codewa
in terms of 8 hour days
rate for A alone 2
rate for A & B together 1.25
1/a+1/b=1/x
1/2+1/b=1/1.25
1/b=1/1.25-1/2
1/b=2/2.5-1.25/2.5
1/b=0.75/2.5
1/b=1/3.33333333
b=3.33333333
rate for B alone 3.33333333 8 hour days
check
1/2+1/3.33333333=1/1.25
3.33333333/6.66666667+2/6.66666667=1/1.25
5.33333333/6.66666667=1/1.25
ok
codewa