The filling rate of the first tank is this: [tex] \frac{1 tank}{1 hour} [/tex] The filling rate of the second tank is this: [tex] \frac{1 tank}{2 hours} [/tex] Add them to get the combined rate: [tex] \frac{1 tank}{1 hour} + \frac{1 tank}{2 hours}[/tex] Make a common denominator by multiplying the first fraction by 2/2: [tex] \frac{2 tanks}{2 hours} + \frac{1 tank}{2 hours} [/tex] Adding them together, we get: [tex] \frac{3 tanks}{2 hours} [/tex]
So, now we know that the combined rate is 3 tanks per 2 hours... but we need to know how long it will take to fill only one tank. So, we need to find the unit value, which we do by doing this: [tex] \frac{3}{2} = \frac{1}{x} [/tex] Then we can cross-multiply: [tex]3x = 2[/tex] And divide both sides by 3 to get our final answer: [tex]x = \frac{2}{3} [/tex]
So, it takes 2/3 of an hour, or 40 minutes.
Hope I helped, let me know if you have any questions :)
