Janus with Danus

Its pretty simple if you just don't get confused by "12 of Danus" . It is just a question on fractions. 12 people, 18 burgers, 2 hours : so simply workrate is 18/(2 12) = 3/4 . Similarly second workrate is 60/(6 15) = 2/3 . Hence total workrate is 2/3 + 3/4 = 17/12 . So answer is 17+12 = 29 .

Work rates can be shown as this:

$\dfrac{\text{\# of hamburgers eaten}}{\text{\# of people}\times\text{\# of hours}}$

So the work rate of Danus is $\dfrac{18}{12\times2}$ and the work rate of Janus is $\dfrac{60}{15\times6}$

Simplify: $\dfrac{9}{12}$ and the work rate of Janus is $\dfrac{4}{6}$

Again: $\dfrac{3}{4}$ and the work rate of Janus is $\dfrac{2}{3}$

Now the work rate of both is basically adding the two work rates. So that $\dfrac{3}{4} + \dfrac{2}{3}$ is the work rate of both. That would equal $\dfrac{9}{12} + \dfrac{8}{12} = \dfrac{17}{12}$ . Now it is asking for a+b, but the fraction $\dfrac{17}{12}$ can be expressed as $\dfrac{a}{b}$ . So

$a = 17 \text{ and } b = 12$

Now we can solve this problem. $a + b = 17 + 12 = \boxed{29}$