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

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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) About Me  (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"
%2820%2F3%29%2Fa + %2820%2F3%29%2Fb = 1
Which is:
20%2F%283a%29 + 20%2F%283b%29 = 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
:
3%2Fa + 45%2F%284b%29 = 1
Multiply the 1st fraction by 3/3 to have same denominator as the 1st equation
9%2F%283a%29 + 45%2F%284b%29 = 1
;
Try to use elimination here with these two equations:
9%2F%283a%29 + 45%2F%284b%29 = 1
20%2F%283a%29 + 20%2F%283b%29 = 1
:
Multiply the 1st equation by 20, and the 2nd equation by 9, results:
180%2F%283a%29 + 900%2F%284b%29 = 20
180%2F%283a%29 + 180%2F%283b%29 = 9
---------------------------------------subtraction eliminates a, leaving:
900%2F%284b%29 - 180%2F%283%29 = 11
225%2Fb - 60%2Fb = 11; reduced the fractions
165%2Fb = 11
b = 165%2F11
b = 15 hrs by himself
:
Find a using eq: 20%2F%283a%29 + 20%2F%283b%29 = 1;
20%2F%283a%29 + 20%2F%283%2A15%29 = 1;
20%2F%283a%29 + 20%2F45 = 1;
20%2F%283a%29 + 4%2F9 = 1; reduced the fraction
20%2F%283a%29 = 1 - 4%2F9%29
20%2F%283a%29 = 5%2F9%29
Cross multiply
5(3a) = 20*9
15a = 180
a = 180%2F15
a = 12 hrs by himself
:
:
Check solution using eq;9%2F%283a%29 + 45%2F%284b%29 = 1
9%2F%2836%29 + 45%2F%2860%29 = 1
1%2F4 + 3%2F4%29 = 1; confirms the solutions to this horrible problem!