I am not sure the unit you are supposed to use - kf og is not a known unit to me
It was clearly intended to be "kf
rog", a unit equal to the weight of a thousand frogs!
As Subhotosh Kahn suggested, call the original weight of Jake's pack, J, and the original weight of Robyn's pack, R.
But this is, unfortunately a very poorly worded problem! Was it translated from another language?
After they have gone 15KM they swap packs and discover that Jake's Original pack is twice as heavy.
Jake's pack is twice as heavy as Robyn's original pack so J= 2R.
They transfer 6kf of food from Robyn's new pack to Jake's new pack,
So Robyns pack is now 6 "thousand frogs" lighter, or R- 6. Jakes new pack is 6 heavier, or J+ 6.
so that when they have completed the final 25KM, the total weight and distance will be the same for each person.
Normally, "total" means the sum but since "weight" and "distance" have different units so adding them would make no sense. I think what is intended is total "weight
times distance". Jake carried pack weight J for 15 km and then carried J+ 6 for 25 km for a total of 15J+ 25(J+ 6)= 40J+ 150. Robyn carried pack weight R for 15 km then carried R- 6 for 25 km so a total of 15R+ 25(R- 6)= 40R- 150. In order that those be equal, we must have 40J+ 150= 40R- 150 which simplifies to J= R- 15/2
Write an equation to find the original weight of each pack, then solve for the original weight.
You have J= 2R and J= R- 15/2 so 2R= R- 15/2, R= -15/2.
That, a negative weight, makes no sense at all! Looking back at the problem, Robyn's pack is heavier but to make even, they transfer weight
from Jake
to Robyn! That's what makes the problem non-sense. If, as I am sure was intended, they transferred 6 kf
from Robyn
to Jake, then the second equation becomes R= J- 15/2 so that R= 2R- 15/2, R= 15/2 kf, J= 15 kf.
(Seriously, I assume the "k" in "kf" is "kilo" but what is the "f"?)