SOLUTION: Mr.X can finish a job in nine hours. After working for five hours, he decided to stop. Mr.Y helped Mr. X and finished the job in 2 hours and 20 minutes. How long would it take Mr.

Click here to see ALL problems on Linear Algebra

Question 915668: Mr.X can finish a job in nine hours. After working for five hours, he decided to stop. Mr.Y helped Mr. X and finished the job in 2 hours and 20 minutes. How long would it take Mr. Y to do the job alone?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39614) (Show Source):
You can put this solution on YOUR website!
RATES AS JOBS per HOUR
Mr. X,
Mr. Y,
Mr. X&Y,

The one whole job done:
.

The reason the equation is composed that way is because Mr. X (he) decided to stop. When Mr. Y helped, he and Mr. X were not working on the job at the same time.

Solve the equation for y.

HOURS for Mr. Y to do the job alone.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Mr.X can finish a job in nine hours. After working for five hours, he decided to stop. Mr.Y helped Mr. X and finished the job in 2 hours and 20 minutes. How long would it take Mr. Y to do the job alone?
-----
X's rate:: 1/9 job/hr
------------------
In 5 hrs X does 5/9 of the job.
=====
Let Y's time to do the job alone be "x"; his rate is 1/x job/hr
----
Note:: 2 hr and 20 min = 2 hr and (1/3)hr = 7/3 hrs.
---------------------------------------------------
Together rate is 1/(7/3) = 3/7 job/hr
-----
Equation to solve for "x":
work + work = 1 job
---
(5/9)+ (1/9 + 1/x)(3/7) = 1 job
------
[(x+9)/x](3/7) = 4/9
(x+9)/x = (4/9)(7/3)
(x+9)/x = 28/27
28x = 27x+9*27
x = 81 hrs (time for "y" to do the job alone)
================
Cheers,
Stan H.
------------------