96' 
THE APPLICATION OF ALGEBRA 
— a -f b — c, and 
a f b — c 
de -f 2d 4- 1 
— 7. Therefor^ 
x {— dz — b) zz 16; y (— dz -f c) rr 25; and. 
u ( rr dcz) — 42. 
PROBLEM XXXVI. 
//A and B together, can perform a piece o f work in 
8 fa J days; A and C together in 9 fbj days, and B and 
C in 10 (c) days; how many days will it take each per 
son, alone, to perform the same work f 
Let the three numbers sought be represented by x, 
y, and z, respectively; then it will be, as r (days) : a 
(days) :: l, the whole work, to , the part thereof 
performed by A in a days; and, as y : a :: 1 : the 
part performed by B, in the same time; whence, by the 
question, ~ ~ + (the whole work). And, by 
x 
proceeding in the very same manner, we shall have 
these two other equations, viz. — 4- —— r: l, and 
C c • 
— + — =: l: let the first of these three equations 
y z * 
be divided by a, the second by b, and the third by c, 
you will then have 
which added all together, and the sum divided by 2,give 
1 
7 
i 
i 
ila 
from