SOLUTION: if a girl works for 8mins and her brother works for 15mins, they can wash the front windows of their house. also, if the girl works for 12 mins and her brother works for 10mins, th

Question 408399: if a girl works for 8mins and her brother works for 15mins, they can wash the front windows of their house. also, if the girl works for 12 mins and her brother works for 10mins, they can wash the same windows.how long will it take each person to wash the windows?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
if a girl works for 8mins and her brother works for 15mins, they can wash the front windows of their house. also, if the girl works for 12 mins and her brother works for 10mins, they can wash the same windows.how long will it take each person to wash the windows?
..
let 1/x=minute work rate of girl (this means working alone, she would complete the job in x minutes)
let 1/y=minute work rate of boy (this means working alone, he would complete the job in y minutes)
first situation:
8(1/x)+15(1/y)=100%
second situation:
12(1/x)+10(1/y)=100%
To solve:
let u=1/x
let v=1/y
then:
8u+15v=1
12u+10v=1
multiply first equation by 6, and second equation by -4
48u+90v=6
-48u-40v=-4
add equations
50v=2
v=2/50=1/25=1/y
or y=25 minutes
solving for u
8u+15(1/25)v=1
200u+15=25
200u=10
u=1/20=1/x
or x=20 minutes
ans:
Working alone the girl will finish washing the windows in 20 mimutes
Working alone the boy will finish washing the windows in 25 mimutes

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