SOLUTION: Gian and Arwin can finish a project in 4 2/3 hours. Gian can do it alone in half as much as time arvin can do the job. how long will it take arwin to do the job alone.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Gian and Arwin can finish a project in 4 2/3 hours. Gian can do it alone in half as much as time arvin can do the job. how long will it take arwin to do the job alone.      Log On


   

Question 149525: Gian and Arwin can finish a project in 4 2/3 hours. Gian can do it alone in half as much as time arvin can do the job. how long will it take arwin to do the job alone.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=rate (projects per hour) at which Arvin works
Then 2x=rate at which Gian works (works twice as fast)
Together they work at the rate of x+2x=3x projects per hour
But we are told that together, they work at the rate of 1/(4 2/3) projects per hour= 3/14 projects per hour. So our equation to solve is:
3x=3/14 divide each side by 3
x=1/14 project per hour----------------rate at which Arvin works
Now if z=amount of time it takes Arvin to do the project, then
(1/14)*z=1 (1 project, that is)
z=14 hours---------------amount of time it takes Arvin working alone
Also:
2x=2(1/14)=2/14 projects per hour-------------------rate at which Gian works
CK
1/14 + 2/14=1/(4 2/3)=1/(14/3)=3/14
3/14=3/14
Hope this helps---ptaylor