Answered

Magtanong at makakuha ng maliwanag na mga sagot sa IDNStudy.com. Tuklasin ang mga maaasahang impormasyon sa anumang paksa sa pamamagitan ng aming network ng bihasang mga propesyonal.

Ann and Mary together can do a piece of work in 4 days. Ann and Naty can do the work in 6 days. Mary and Naty can do it in 5 days.how long would it take each to do the work ?

Sagot :

Shinalcantaraidn
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
Mariamikaylaidn
[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]