college algebra word problem

Question

i am stuck on the following problem. here is a pic of the problem

http://imgur.com/CvLAT0P

any help would be appreciated

Answer 1

A fills the tank

B drains the tank

let x=# of hours it takes A to fill the tank

let x+5=# of hours to drain the tank

each hour A fills (1/x) of the tank

each hour B drains(1/[x+5]) of the tank

with both pipes open it takes 10 hours to fill the tank

the pipes are working against each other and not with each other

(1/x)(10)-(1/[x+5])(10)=1 (tank filled)

multiply both sides by (x)(x+5)

(x)(x+5)(1/x)(10)-(x)(x+5)(1/[x+5])(10)=(x)(x+5)(1)

simplify

(x+5)(10)-(x)(10)=(x)(x+5)

10x+50-10x=x²+5x

50=x²+5x

x²+5x-50=0

(x+10)(x-5)=0

x-5=0

x=5 hours for A to fill the tank alone

x+5=5+5=10 hours for B to drain the tank alone (if A is closed)

check: each hour A fills 1/5 of the tank while B drains 1/10 of the tank for a net fill of (1/5)-(1/10)=(2/10)-(1/10)=1/10 of the tank filled; in other words, after one hour with both pipes open, 1/10 of the tank gets filled and after 10 hours the tank is full, which is what was stated: it takes 10 hours to fill the tank with both pipes open !

after 5 hours A fills 5/5 and B drains 5/10 for a net fill of 1- 1/2=1/2 of the tank filled