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) (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!
