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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
