Magtanong at makakuha ng maaasahang mga sagot sa IDNStudy.com. Makakuha ng hakbang-hakbang na mga gabay para sa lahat ng iyong teknikal na tanong mula sa mga miyembro ng aming komunidad na may kaalaman.
Sagot :
let 'x' be the rate of Ann to finish the job
'y' be the rate of Mary
'z' be the rate of Naty
x(4) + y(4) = 1
4x + 4y = 1 ----equation 1
x(6) + z(6) = 1
6x + 6z = 1 ----equation 2
y(5) + z(5) = 1
5y + 5z = 1 ----equation 3
multiply equation 1 with 6 and equation 2 with 4
4x + 4y = 1
24x + 24y = 6 -----equation 1'
6x + 6z = 1
24x + 24z = 4 -----equation 2'
subtract equation 2' from equation 1'
24y - 24z = 2
dividing the whole equation by 2
12y - 12z = 1 ------equation 4
multiply equation 3 with 12 and equation 4 with 5
5y + 5z = 1
60y + 60z = 12 ----equation 3'
12y - 12z = 1
60y - 60z = 5 -----equation 4'
add equation 4' and equation 3'
120y = 17
y = 17/120
substitute the value of y to equations 1 and 3
4x + 4y = 1
4x + 4(17/120) = 1
4x = 1 - 68/120
4x = 13/30
x = 13/120
5y + 5z = 1
5(17/120) + 5z = 1
5z = 1 - 85/120
5z = 7/24
z = 7/120
to get the time for each to finish the job alone, get the reciprocal of the rates.
y = 17/120
t(y) = 120/17 days
t(y) = 7.06 days
x = 13/120
t(x) = 120/13 days
t(x) = 9.23 days
z = 7/120
t(z) = 120/7 days
t(z) = 17.14 days
'y' be the rate of Mary
'z' be the rate of Naty
x(4) + y(4) = 1
4x + 4y = 1 ----equation 1
x(6) + z(6) = 1
6x + 6z = 1 ----equation 2
y(5) + z(5) = 1
5y + 5z = 1 ----equation 3
multiply equation 1 with 6 and equation 2 with 4
4x + 4y = 1
24x + 24y = 6 -----equation 1'
6x + 6z = 1
24x + 24z = 4 -----equation 2'
subtract equation 2' from equation 1'
24y - 24z = 2
dividing the whole equation by 2
12y - 12z = 1 ------equation 4
multiply equation 3 with 12 and equation 4 with 5
5y + 5z = 1
60y + 60z = 12 ----equation 3'
12y - 12z = 1
60y - 60z = 5 -----equation 4'
add equation 4' and equation 3'
120y = 17
y = 17/120
substitute the value of y to equations 1 and 3
4x + 4y = 1
4x + 4(17/120) = 1
4x = 1 - 68/120
4x = 13/30
x = 13/120
5y + 5z = 1
5(17/120) + 5z = 1
5z = 1 - 85/120
5z = 7/24
z = 7/120
to get the time for each to finish the job alone, get the reciprocal of the rates.
y = 17/120
t(y) = 120/17 days
t(y) = 7.06 days
x = 13/120
t(x) = 120/13 days
t(x) = 9.23 days
z = 7/120
t(z) = 120/7 days
t(z) = 17.14 days
[tex]A+M=4 \\ A+N=6 \\ M+N=5 \\ ======= \\\\ 2A+2M+2N=4+6+5 \\\\ 2(A+M+N)=15 \ |:2 \\\\ A+M+N=7.5\\ A+M=4 \\\\ =>N=7.5-4 \ \ \to\boxed{N=3.5 } \ (3 \ days \ and \ a \ half \ for \ Naty) \\\\\\ A+M+N=7.5 \\ A+N=6 \\ \\ => M=7.5-6 \ \ \to\boxed{M=1.5} \ (1 \ day \ and \ a \half \ for \ Mary) \\\\\\ A+M+N=7.5 \\ M+N=5 \\ \\ => A=7.5-5 \ \ \to\boxed{A=2.5} \ (2 \ days \ and \ a \ half \ for \ Ann)[/tex]
Salamat sa iyong kontribusyon. Huwag kalimutang bumalik upang magtanong at matuto ng mga bagong bagay. Ang iyong kaalaman ay mahalaga sa ating komunidad. Sa IDNStudy.com, kami ay nangako na magbigay ng pinakamahusay na mga sagot. Salamat at sa muling pagkikita.