Makakuha ng mabilis at tumpak na mga sagot sa iyong mga katanungan sa Imhr.ca, ang pinakamahusay na Q&A platform. Tuklasin ang aming Q&A platform upang makahanap ng malalim na sagot mula sa isang malawak na hanay ng mga eksperto sa iba't ibang larangan. Kumuha ng mabilis at mapagkakatiwalaang mga solusyon sa iyong mga tanong mula sa isang komunidad ng mga bihasang eksperto sa aming platform.
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]
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