SOLUTION: A and B working together can do a job in 20/3 hours. A became ill after 3 hours of working with B and B finished the job, continuing the work alone in 33/4 more hours. How long wou

Question 162431: A and B working together can do a job in 20/3 hours. A became ill after 3 hours of working with B and B finished the job, continuing the work alone in 33/4 more hours. How long would it take each working alone to do the job????
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A and B working together can do a job in 20/3 hours. A becames ill after 3 hours
of working with B and B finished the job, continuing the work alone in 33/4 more
hours. How long would it take each working alone to do the job????
:
Let a = A's time working alone
Let b = B's time working alone
Let the completed job = 1
:
Equation 1, for the statement,"A and B working together can do a job in 20/3 hours"
+ = 1
Which is:
+ = 1; (we invert the dividing fraction and multiply)
:
Equation 2 when A gets sick:
B works 3 hr + 33/4 hr = 45/4; hrs total for B
:
+ = 1
Multiply the 1st fraction by 3/3 to have same denominator as the 1st equation
+ = 1
;
Try to use elimination here with these two equations:
+ = 1
+ = 1
:
Multiply the 1st equation by 20, and the 2nd equation by 9, results:
+ = 20
+ = 9
---------------------------------------subtraction eliminates a, leaving:
- = 11
- = 11; reduced the fractions
= 11
b =
b = 15 hrs by himself
:
Find a using eq: + = 1;
+ = 1;
+ = 1;
+ = 1; reduced the fraction
= 1 -
=
Cross multiply
5(3a) = 20*9
15a = 180
a =
a = 12 hrs by himself
:
:
Check solution using eq; + = 1
+ = 1
+ = 1; confirms the solutions to this horrible problem!

RELATED QUESTIONS
A and B working together can do a job in 6 2/3 hours. A became ill after 3 hours of... (answered by josmiceli)

"This is the problem. Would you please help me with this? Thank You!" ---> A and B... (answered by ankor@dixie-net.com)

A and B working together can finish a certain job in 20/3 hours. They start the work... (answered by stanbon)

Persons A and B, working together, can do a job in 6 2/3 hours. A became ill after... (answered by macston)

If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work,... (answered by ankor@dixie-net.com,vipower)

1.) Sketch the graph of{(x,y)absolute value x-y=3 and x+2y>4} 2.) Sketch the graph of... (answered by Theo)

A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B... (answered by ankor@dixie-net.com)

A and B working together can finish the job alone in 3 hours , while A can finish the job (answered by jorel1380,MathTherapy)

Hi, I would really appreciate help with this problem: George and Michael working... (answered by stanbon)