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Julia and Heiko are two enthusiastic caching sparrows. Therefore, when a new cache is published nearby, they both leave their nests immediately. The cache hiding place is located exactly on the midpoint of the line joining their two nests. Heiko lives to the east and Julia to the west of the hiding place. In the absence of any wind, both can fly at a speed of 60 km/h . However, on this day, there is a strong wind from the east, blowing with a speed of 44 km/h. This causes Julia's arrival to be one minute later than Heiko, whom, by this time, is already on his way back to his nest which is located at N 52° 30.098 E 13° 22.547. The question is where is the midpoint?

Gerry9999
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  • Welcome to MSE. Is there a question here? – José Carlos Santos Nov 22 '19 at 11:37
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    Welcome to Math.SE! The community here prefers/expects questions to include something of what the asker knows about the problem. (What have you tried? Where did you get stuck? etc) This information helps answerers tailor their responses to best serve you, without wasting time (theirs or yours) telling you things you already know or talking over your head. (It also helps convince people that you aren't simply trying to get them to do your homework for you.) Since comments are easily overlooked, edit your question to add details. – Blue Nov 22 '19 at 11:40
  • Sorry guys. The question is where is the midpoint? – Gerry9999 Nov 22 '19 at 11:54
  • Gerry9999, I will be more blunt than @Blue - Most of us don't enjoy just doing your homework for you. However, many of us enjoy teaching or giving hints on how to do homework. That's why you need to show us some effort first... – antkam Nov 22 '19 at 18:02
  • Thanks for your response and I wish it was my homework but at 74 years old I can't remember back that far. It's actually a Geocaching puzzle in Berlin called Gegenwind GC1VYR7. I have tried to solve using https://www.symbolab.com/solver/algebra-calculator and y=mx+c but I really don't have a clue. So it's over to you I am at you mercy. Greetings from Ireland Gerry Needless to say I can work out the final coordinates if I could find the distance traveled by Keiko. – Gerry9999 Nov 22 '19 at 18:43

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Gerry: sorry for being blunt and presumptious about this being homework... :(

Anyway, let $x$ km be the distance from either nest to the midpoint. Heiko is flying at $60+44 = 104$ km/h and Julia at $60-44 = 16$ km/h. So Heiko got there at time $x/104$ (hr) and Julia got there at time $x/16$ (hr). We are given that Julia is late by one minute, i.e.

$${x \over 104} + {1 \over 60} = {x \over 16}$$

which solves to $x = {52 \over 165}$ km.

antkam
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