Bronquinha can mow the lawn in his backyard in 3 hours, but if he drinks Gummy fruit juice, he mows in 2 hours. On a certain day, Bronquinha started mowing the lawn at 10:00 AM and, at some point, drank the Gummy fruit juice, finishing mowing the lawn at 12:30 PM. What time did Bronquinha drink the Gummy fruit juice?

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Solution

Let $A$ be the area of grass to be mowed. Thus, without drinking the juice, the speed at which

Bronquinha mows the grass is $\frac{A}{3}$, while with the juice, the speed is $\frac{A}{2}$. Let $t$ be the time that Bronquinha mows the grass without drinking the juice, in the proposed situation, we have:

$$
\begin{aligned}
\frac{A}{3} \cdot t+\frac{A}{2} \cdot(2.5-t) & =A \\
\frac{t}{3}+\frac{2.5-t}{2} & =1 \\
2 t+7.5-3 t & =6 \\
t & =1.5
\end{aligned}
$$

Therefore, if Bronquinha started mowing the grass at $10 \text{ AM}$, he drank the juice at 11:30 AM.