Question

If Calvin and Bonzo eat together,they can eat $480$ hot dogs in $6$ hours.Eating alone, Bonzo takes $16$ hours longer than Calvin would to eat $480$ hot dogs. How many hours does it take Calvin to eat $480$ hot dogs?

Answer 1

Let Calvin can eat hot dogs be x.
Bonzo can eat hot dogs be y.
t represents the time taken to eat hot dogs.
As per the data we have drawn the tabular column.
So, Calvin and Bonzo can eat together = 6(x + y) = 480 ---- (1)
Calvin alone eat = tx = 480 --- (2)
Bonzo eating alone = (t + 16)y = 480 ----- (3)
Substituting the value of $x$ and $y$ in equation (1)
$\Rightarrow 6(\frac{480}{t}+\frac{480}{t+16})=480$
$\Rightarrow \frac{480}{t}+\frac{480}{t+16}=80$
$\Rightarrow t(t+16).(\frac{480}{t}+\frac{480}{t+16})=t(t+16).80$
$\Rightarrow 480(t+16)+480t=80t(t+16)$
$\Rightarrow 6(t+16)+6t=t(t+16)$
$\Rightarrow 6t+96+6t=t^2+16t$
$\Rightarrow 0=t^2+4t-96$
$\Rightarrow 0=(t+12)(t-8)$
$\therefore t=-12,8$
Since t can't be negative, the answer is $t=8$ hours.
Therefore, Calvin take 8 hours to eat $480$ hot dogs.