TO THE RESOLUTION OP PROBLEMS, 9? 
H 
whence each of the three last equations being succes* 
sively subtracted, we get 
1 _ 1 1 1 _ be + ac + ab 
z 2a 2b 2c ~ 2abc * 
i _ _1 1 I __ be — ac + ab 
y ~ 2a 2 b 2 c ~~ 2 abc 
-*- = J- + _L L = te 4 ac-ab_ Hence 
x 2a 2b 2c 2abc 
2 abc 
1440 
be 
be + ac + ab ~ — 90 + 80+72 
2 abc _ 1440 
— ac + ab 
- 23*, 
90 
-80+72 
___ 1440 
be + ac — ab ~~ 90 + SO — 72 
2abc 
= 17H. 
= 14^. 
Otherwise, 
Let the work performed by A in one day be de 
moted by 07: then his work in a days will be ax, and in 
b days it will be bx ; therefore the work of B in a days 
will be 1 — ax; and that of C, in b days, 1 — bx, by 
the conditions of the problem; whence it follows 
that the work of B, in one day, will be expressed by 
-— an d that of C, in one day, by -—; but 
i 
the sum of these two last is, by the question, equal to — 
part of the whole work, that is, ~~ + — 2a? = ~ § 
whence x 
JL +JL 
2 a 2 b 
JL 
2C 
b 
ôc + ac- 
•ab 
2 abc 
, equal 
to the work done by A in one day; by which divide 
1 (the whole) and the quotient, ¿ c ab* 
the required number of days in which he can finish the 
whole,