# 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 ?

2
by akoto1423

2014-10-25T22:47:59+08:00
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
2014-10-26T07:22:51+08:00

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.