SOLUTION: allan can finish a set of furniture in 8 days. ben can finish the same set of furniture in 6 days. if allan starts working for 2 days, and then ben joined him, in how many days wil

Click here to see ALL problems on Rate-of-work-word-problems

Question 213071: allan can finish a set of furniture in 8 days. ben can finish the same set of furniture in 6 days. if allan starts working for 2 days, and then ben joined him, in how many days will the set of furniture be finished by the two men?
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
allan can finish a set of furniture in 8 days.
ben can finish the same set of furniture in 6 days.
if allan starts working for 2 days, and then ben joined him,
in how many days will the set of furniture be finished by the two men?
:
let t = time working together
:
Let the completed job = 1
:
+ = 1
Multiply equation by 24, results
3(t+2) + 4t = 24
3t + 6 + 4t = 24
3t + 4t = 24 - 6
7t = 18
t =
t = 2.57 days working together
;
:
Check
+ =
.57 + .43 = 1

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
allan can finish a set of furniture in 8 days. ben can finish the same set of furniture in 6 days. if allan starts working for 2 days, and then ben joined him, in how many days will the set of furniture be finished by the two men?
--------------------------------------------
Allan's Rate = 1/8 days/job
-----------------------------
Ben's Rate = 1/6 days/job
-----------------------------
Allan works for 2 days and finished 2(1/8) = 1/4 th of the job.
--------
Equation:
Together rate = (1/8 + 1/6) = 14/48 = 7/24 job/day
-----------------------------------------------------------
Let x be the number of days for allan and ben to finish 3/4 th of the job.
--
x(7/24) = 3/4
x = (24/7)(3/4)
x = 18/7 = 2 4/7 days
==================================
Cheers,
Stan H.