SIMPLE ECUJATIONS. 35 i 



That IS, \-x=±i2f or i3a:*j-io;;= 13d ; 



And therefore 23^= 130, or ;tf = '-^ = 5-|^ days, the time 

 required. 



1 1. If one agent A alone can produce an effect e in the 

 time a, and another agent B alone in the time if 5 in what 

 time will they both together produce the same effect ? 

 Let the time sought be denoted by x. 



Then a : e : : » : — =1 part of the effect produced by Av 



And h : e :-. X : -y-zr: part of the effect produced by B, 



ex ex 

 Whence \--r=zehy the question j 



X X 



Or -+-=:, 



That IS, x-f-yzi^ia ; 



Or bx'^-ax-^iha ; 



ba 

 And consequently, y — y~p--= time required. 



QUESTIONS FOR PRACTICE. 



1. What two numbers are those, whose difference is 7, 

 and sum 33 ? Ans. 13 and 20. 



2. To divide the number 75 into two such parts, that 

 three times the greater may exceed seven times the less by 

 15. Ans. 54 and 21. 



3. In a mixture of wine and cider, ~ of the whole plus 

 25 gallons was wine, -|. part minus 5 gallons was cider ; 

 how many gallons were there of each ? 



Ans. 85 of wine and 35 of cider. 



4. A 



