The doe family is ready to fill their new swimming pool. it can be filled in 12 hours if they use their own water hose, and in 30 hours if they use mr. jones', their neighbor's water hose. how long will the doe's take to fill their pool if the neighbor's hose is used along with their own?

6 & 1/2 hours should be the correct answer! :]

Doe's swiming pool can be filled in 12 hours
so doe's rate is 1/12 pool per hour
basicallly, in 1 hour, 1/12 of the pool if filled

the jonesles take 30 hours
so 1/30 pool per hour
basically in 1 hour, 1/30 of the pool is filled

so 

combined
1/12+1/30
find common denom
12=2*2*3
30=2*3*5
common denom=2*2*3*5=60

1/12 times 5/5=5/60
1/30 times 2/2=2/60
so

add the rates
in 1 hour, a total of 1/12+1/30 or 5/60+2/60=7/60 pool per hour

so
7/60 pool per hour

amount=rate times time
we want 1 pool to be filled
rate is 7/60 pool per hour
t=time

1=7/60 pool per hour times t
times both sides by 60/7
60/7=t
8.57142857143=t
takes about 8.57 o 8.6 hours