SOLUTION: a carpenter can build a desk in 32 hours. After 8 hour he is joined by a second carpenter who could build the desk in 40 hours. How long does it take them to complete the desk work

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a carpenter can build a desk in 32 hours. After 8 hour he is joined by a second carpenter who could build the desk in 40 hours. How long does it take them to complete the desk work      Log On


   

Question 954952: a carpenter can build a desk in 32 hours. After 8 hour he is joined by a second carpenter who could build the desk in 40 hours. How long does it take them to complete the desk working together.
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Carpenter A: 1 desk/32hrs builds 1/32 desk per hour=0.03125 desk/hr
Carpenter B: 1 desk/40hrs builds 1/40 desk per hour=0.025 desk/hr
In 8 hours Carpenter A builds 8(0.03125)desk or 0.25 desk.
Carpenter B joins with 0.75 desk to go.
Together they build 0.03125+0.025=0.05625 desk/hr
0.75 desk/0.05625 desk/hr=13.33 hours
ANSWER: It should take the two together 13.33 hours to finish the desk.

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Carpenter, 1%2F32
Second Carpenter, 1%2F40
Both Together, 1%2F32%2B1%2F40

Manage denominators later.

RT=J, where J is how many desks or desk, rate R, time T.
A uniform work rates situation.

%281%2F32%298%2B%281%2F32%2B1%2F40%29t=1.
That is what you want to be able to say. t is the amount of time that both carpenters work together while finishing the desk.
Now, you can multiply the left and right members of the equation by lowest common denominator and continue simplification to solve for t.


LCD is 2%2A2%2A2%2A2%2A2%2A5.