Question

An application of a rational function is T = (AB)/(A+B), which gives the time, T, it takes for two workers to complete a particular task where A & B represent the time it would take for each individual worker to complete the identical task working alone. It takes William 3 hours longer than Timothy to paint a 4x 5 feet bedroom. Respond to the following:

Working together, both can complete the job in 2 hours. How long does it take each one to complete the painting job working alone?
Provide a similar example, set up the equation and solve the problem.
Show you work step by step

Answer 1

let it take William A hours to complete the work, and Timothy B hours,
It takes William 3 hours longer than Timothy to paint a 4x 5 feet bedroom. ---> A=B+3 ---->(1)
Working together, both can complete the job in 2 hours.
-----> (AB)/(A+B) = 2 ---->>(2)
can you solve those 2 equations simultaneously to get values of A and B ??

Answer 2

i have no idea where to even start. I have been trying to figure this problem out for at least a hour

Answer 3

thats what exactly i gave you, a start...didn't you get how those 2 equation i formed ?

Answer 4

yes so when they work together there hours are 1hr each

Answer 5

so A=1 and B=1

Answer 6

how you got that ?? no, its incorrect...

Answer 7

thats my problem I do not know where to get their hours from

Answer 8

from (1) you have A =B+3
put this A in equation (2),
then you'll have a equation only in terms of B, so that you can find it.

Answer 9

how do I find the value of A

Answer 10

first could you find B ?
then A is just B+3

Answer 11

(AB)/(A+B) = 2
((B+3)B) = 2 (B+3+B)

Answer 12

\[\frac{ (3+b)b }{3+b+b }= \frac{ 3b+b^{2} }{3+2b }\]

Answer 13

you'll get a quadratic in B

Answer 14

that looks complicated..
try this,
((B+3)B) = 2 (B+3+B)

Answer 15

\[-b^{2}+b+6\]

Answer 16

now i need to factor it

Answer 17

b^2+3b=4b+6
b^2-b-6=0
this form will be easier, and yes, factor it.

Answer 18

(b-2)(b-3)

Answer 19

B=2 or B=3

Answer 20

b^2-b-6=0
(b+2)(b-3) = 0
b=-2 , b= 3
but b is time and it cannot be negative,
so b=3
got this ?

Answer 21

yes

Answer 22

so, timothy takes 3 hours, and william will take 3+3 =6 hours, righ ?

Answer 23

yes

Answer 24

can you provide similar example on your own ? just change numbers....

Answer 25

ask if any doubts

Answer 26

i think I can now. i think what confused me was the example my teacher put up of this

Answer 27

good...