Distance and speed of two people walking 100 miles

Question

This is for GRE math prep. Can you explain why the answer to this is 54? Five hours after Sasha began walking from A to B, a distance of 100 miles, Mario started walking along the same road from B to A. If Sasha's walking rate was 2 miles per hour and Mario's was 3 miles per hour, how many miles had Mario walked when they met?

[ ] 42
[ ] 46
[X] 54
[ ] 58
[ ] 64

I know the formula $$Rate=\frac{Distance}{Time}$$ but not sure how to use it here to solve this. Do you have a general rule for helping solve these mind-twisting word puzzles? Thank you.

Answer 1

Let $t$ be the number of hours that Mario walks before they meet. Then Sasha has walked $5+t$ hours, and $$2(5+t)+3t=100.$$

Or else, without "algebra": Sasha has walked $10$ miles before Mario sets out, so at that time they are $90$ miles apart. Then distance between them shrinks $5$ miles per hour, so it takes $18$ hours to shrink to $0$.

Answer 2

Let M be mario's distance and let S be Sasha's distance. Then $ S = 2t$ and $M = 100 - 3(t-5)$. Equate them and you have $2t = 100 - 3(t-5)$ simplifying gives $5t = 113$ thus $t = 23$. Thus mario has walked 3*(23-5) = 54 miles.