# Math Help - How to calculate the Point of equal time between departure and destination?

1. ## How to calculate the Point of equal time between departure and destination?

Hi this is propably really simple but i can't understand it.

PET or point of equal time is a term used in aviation. It defines a point along a route where the time to continue is the same as the time to return to the aerodrome of departure. I have a hard time understanding how it is calculated in my book that i use in school.
This is how they explain it:

dpet= the distance to the pont of equal time
GSr=The groundspeed to return from PET to departure
GSo=the groundspeed to continue from the PET to destination
D=the total distance between departure and destination

time home from PET=time on from PET

dpet/GSr=(D-dpet)/GSo
So far I understand but what i don't understand is how they have transposed the formula to dpet=D*GSr/(GSo+GSr)

2. ## Re: How to calculate the Point of equal time between departure and destination?

Originally Posted by alban
Hi this is propably really simple but i can't understand it.

PET or point of equal time is a term used in aviation. It defines a point along a route where the time to continue is the same as the time to return to the aerodrome of departure. I have a hard time understanding how it is calculated in my book that i use in school.
This is how they explain it:

dpet= the distance to the pont of equal time
GSr=The groundspeed to return from PET to departure
GSo=the groundspeed to continue from the PET to destination
D=the total distance between departure and destination

time home from PET=time on from PET

dpet/GSr=(D-dpet)/GSo
So far I understand but what i don't understand is how they have transposed the formula to dpet=D*GSr/(GSo+GSr)

$\frac{dpet}{GSr}=\frac{D-dpet}{GSo}$

$\frac{dpet \cdot GSo}{GSr}=D-dpet$

$dpet \cdot GSo=(D-dpet) \cdot GSr$

$dpet \cdot GSo=D \cdot GSr - dpet \cdot GSr$

$dpet \cdot GSo + dpet \cdot GSr=D \cdot GSr$

Now factor out dpet on LHS and afterwards divide through by the bracket.

3. ## Re: How to calculate the Point of equal time between departure and destination?

Thanks earboth!
Exactly what i was looking for. It's scary how fast it's forgotten when you don't use it.