Tanzi and Maeve each have brand new $1200$ mL bottles of soap. They use soap at different constant rates. When Tanzi's bottle is completely empty, she asks Maeve to add soap from Maeve's bottle, which is still two-thirds full. How many milliliters of soap should Maeve pour from her bottle into Tanzi's so that both bottles will be completely emptied at the same time?
1 - 2/3 ==1/3
1/3 * 1200 ==400 mL used by Maeve
1200 - 400 ==800 mL left in Maeve's bottle.
1200 mL used by Tanzi
Ratio of Tanzi to Maeve's use ==1200 : 400 ==3 : 1
3 + 1 =4 sum of the ratios.
800 / 4 ==200 - the constant
200 x 3 ==600 mL Maeve should pour from her bottle into Tanzi's bottle [which is what you are interested in]
200 x 1 ==200 mL should be left in Maeve bottle
Since the ratio of their use is 3 : 1 ==600 : 200 ==3 : 1 when their bottles would be empty at the same time.