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Algebra Difficulty 4.6 AIME Find the answer Canada

Aria and Bianca walk at different, but constant speeds. They each
begin at 8:00 a.m. from the opposite ends of a road and walk directly
toward the other’s starting point. They pass each other at 8:42 a.m.
Aria arrives at Bianca’s starting point at 9:10 a.m. Bianca arrives at
Aria’s starting point at

Pick one

Solution

Let $A$ be Aria’s starting
point, $B$ be Bianca’s starting
point, and $M$ be their meeting
point.

It takes Aria 42 minutes to walk from $A$ to $M$ and 28 minutes from $M$ to $B$ .

(Note that 9:00 a.m. is 18 minutes after 8:42 a.m., and 9:10 a.m. is 10
minutes after 9:00 a.m..)

Since Aria walks at a constant speed, then the ratio of the distance
$AM$ to the distance $MB$ is equal to the ratio of times, or
$42:28$ , which is equivalent to $3:2$ .

Since it takes 42 minutes for Bianca to walk from $B$ to $M$ , the ratio of distances $AM$ to $MB$ is $3:2$ , and Bianca walks at a constant
speed, then it takes Bianca $\$\frac{3}{2} \times$ 42 = 63 $minutes to walk from$ M $to$ A$.

Therefore, Bianca arrives at Aria’s starting point at 9:45 a.m.

(Note that 9:00 a.m. is 18 minutes after 8:42 a.m., and 9:45 a.m. is 45
minutes after 9:00 a.m..)

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.