Three pilgrims $alpha$ $beta$ $gamma$ plan their journey to pilgrim web site $D$ which occurs to be equidistant from the edges of a right-angled ($90^circ$ in $C$) triangle having $a < b < c$. They work out when touring at fixed speeds $v_a$ $v_b$ $v_c$ they are going to attain vacation spot $D$ similar fastened time $t$ later, if they begin similar time from their places $A$ $B$ $C$.
Write $v$ for ratio $$frac{v_b occasions v_c}{v_a}$$
Two vacationers $X$ and $Y$ begin similar time because the pilgrims from their places $C$ and $B$ to succeed in their vacation spot $A$ through $b$ and $c$. They need to arrive at $A$ very same time because the pilgrims arrive at $D$, they usually additionally journey at fixed velocity.
Query: How a lot quicker should $Y$ journey than $X$ when solely given velocity ratio $v$ as reference?
Some clarifications as requested in feedback:
Whereas it is a geometric puzzle (right-angled triangle), it’s introduced as a bodily one (distances, velocity, time, …). Nevertheless, I’ve not used any models on function.
For pilgrims on pilgrimage, time might be by way of weeks or months, and distances might be by way of tons of and even hundreds of kilometers. Nevertheless it actually doesn’t matter a lot. The vacationers may, so to talk, even be microbes or astronauts, they usually may transfer centimeters or transfer between planets, and time might be by way of seconds or centuries.
Solely the values matter.
You’ll be able to categorical the ‘how a lot quicker’ reply as distinction, or ratio, or in another method for vacationers speeds, say, $v_X$ and $v_Y$.
There appears to be some freedom left in selecting pilgrim speeds. However, the restriction for triangle to be right-angled, and the shortage of models, and requirement similar $t$ for everybody, doesn’t go away freedom in evaluating the vacationers speeds.
Trace:
