SOLUTION: "This is the problem. Would you please help me with this? Thank You!" ---> A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3

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Question 699066: "This is the problem. Would you please help me with this? Thank You!" ---> A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3 hours. A became ill and B continuing the work alone finished it in 33/4 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 finish a certain job in 20/3 hours.
They start the work together, but after 3 hours, A became ill and B continuing the work alone. finished it in 33/4 hours.
How long would it take each working alone to do the job?
:
let a = A doing the job alone
let b = B doing it alone
:
Let the completed job = 1
:
Write a share work equation for the statement:
"A and B working together can finish a certain job in 20/3 hours."
%2820%2F3%29%2Fa + %2820%2F3%29%2Fb = 1
invert the divisor and multiply
20%2F%283a%29 + 20%2F%283b%29 = 1
multiply by 3ab, results
20b + 20a = 3ab
:
" They start the work together but after 3 hours, A became ill and B continuing the work alone, finished it in 33/4 hours. How long would it take each working alone to do the job?"
:
Change 33/4 hrs to 8.25 hrs
B works 3 + 8.25 = 11.25 hrs
3%2Fa + 11.25%2Fb = 1
multiply by ab to clear the denominators
3b + 11.25a = ab
:
Try to use elimination with these two equations
3b + 11.25a = ab
20b + 20a = 3ab
Multiply the 1st equation by 20, multiply the 2nd equation by 3
60b + 225a = 20ab
60b + 60a = 9ab
-----------------subtraction eliminates b
165a = 11ab
divide both side by a
165 = 11b
b = 165/11
b = 11 hrs working alone
:
Find a,
20b + 20a = 3ab
replace b with 11
20(11) + 20a = 3(a*11)
220 + 20a = 33a
220 = 33a - 20a
220 = 13a
a = 220/13
a = 1612%2F13 hrs working alone
:
:
Check this in the 1st work statement equation but we will use decimals instead of those annoying fractions
6.67%2F16.92 + 6.67%2F11 =
.394 + .606 = 1; confirms our solutions