SOLUTION: I still can't get how to answer this question: If a girl works for 8 minutes and her brother works for 15 minutes, they can wash the front windows of their house. Also, if the gir

Algebra ->  Matrices-and-determiminant -> SOLUTION: I still can't get how to answer this question: If a girl works for 8 minutes and her brother works for 15 minutes, they can wash the front windows of their house. Also, if the gir      Log On


   

Question 156820: I still can't get how to answer this question:
If a girl works for 8 minutes and her brother works for 15 minutes, they can wash the front windows of their house. Also, if the girl works for 12 minutes and her brother works for 10 minutes, they can wash the same windows. How long will it take each person alone to wash windows? (Hint: if it takes t minutes for a person to do a job alone, then in 1 minute, the person can do 1/t of the job.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
f a girl works for 8 minutes and her brother works for 15 minutes, they can wash the front windows of their house. Also, if the girl works for 12 minutes and her brother works for 10 minutes, they can wash the same windows. How long will it take each person alone to wash windows?
:
Write two equations and use elimination
Let the completed job = 1
:
8%2Fg + 15%2Fb = 1
12%2Fg + 10%2Fb = 1
:
Multiply the 1st equation by 2, and the 2nd equation by 3:
Subtract the 1st equation from the 2nd
:
36%2Fg + 30%2Fb = 3
16%2Fg + 30%2Fb = 2
--------------------subtraction eliminates b
20%2Fg + 0 = 1
g = 20 min, girl alone
:
Find b using the 1st equation:
8%2F20 + 15%2Fb = 1
Mult equation by 20b
8b + 20(15) = 20b
300 = 20b - 8b
12b = 300
b = 300%2F12
b = 25 min, boy alone
:
:
Check solution in the 2nd equation
12%2F20 + 10%2F25 =
3%2F5 + 2%2F5 = 1