SOLUTION: working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more d
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-> SOLUTION: working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more d
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: working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone? This question is from textbook
You can put this solution on YOUR website! working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?
:
Let a = time required by Alice working alone
Let b = time required by Betty alone
Let the completed job = 1
:
equation when they both work 4 day + = 1
Multiply equation by 3 give us integers to work with + = 3
:
Equation when one got sick; (b worked a total of 2+6.75 = 8.75 + = 1
Multiply equation by 6.5 + = 6.5
:
Use elimination here: + = 6.5 + = 3
-------------------------------subtraction eliminates a, find b = 3.5
3.5b = 43.875
b =
b = 12.5357 days for Betty alone
:
Use + = 3, substitute for b and find a + = 3 + 1.037 = 3 = 3 - 1.037 = 1.963
1.963a = 13
a =
a = 6.6225 days for Alice alone
;
:
To check solutions, use + = 1, substituting for a and b: + = 1
.302 + .698 = 1; confirms our solution
