Question 186439
Let x=amount of water needed
Now we know that the amount of pure antifreeze before the water is added (1 gal) has to equal the amount of pure antifreeze after the water is added (0.60(1+x)), so:

1=0.60(1+x)
1=0.60+0.60x  subtract 0.60 from each side
1-0.60=0.60-0.60+0.60x collect like terms
0.40=0.60x divide each side by 0.60
x=2/3  gal------------------amt of water needed
1=0.60(1 2/3)=0.60*(5/3)
1=1

Hope this helps---ptaylor