maths
posted by Anonymous on .
A and B together can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, in how many days A alone will do the same work

Let the rate at which A works be a; the rate at which B works be b; the rate at which C work be c:
(a + b)*12 = 1
(b + c)*15 = 1
a = 2*c
gives
b + a/2 = 1/15
b = 1/15  a/2
Substituting into the first equation:
(a + 1/15  a/2)*12 = 1
a/2 + 1/15 = 1/12
a/2 = 1/12  1/15 = (1512)/(15*12)
a/2 = 3/(15*12) = 1/(5*12) = 1/60
a = 1/30
The rate at which a works is 1/30 of the work per day; so a will complete the task in 30 days.