Problem: A takes m times as long to do a piece of work as B and C together; B takes n times as long as C and A together; and C takes x times as long as A and B together. Then x, in terms of m and n, is:
Answer Choices:
A. m+n2mn
B. 2(m+n)1
C. m+n−mn1
D. m+n+2mn1−mn
E. mn−1m+n+2
Solution:
A1= m1( B1+C1), B1=n1(C1+ A1),C1=x1( A1+ B1)
∴Am−Bn=B1−A1 and Am+Bn=B1+A1+C2=B1+A1+x2(A1+B1)
∴A1(m+1)=B1(n+1) and A1(m−1−x2)=B1(1−n+x2)
∴BA=n+1m+1 and BA=1−n+2/xm−1−2/x∴n+1m+1=1−n+2/xm−1−2/x∴x=mn−1m+n+2