Solve a linear equation given 2 instances

Ahsome

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Robyn and Jake go on a hiking trip. Robyn starts off carrying the pack with the tend and sleeping bags, and Jake stars with the one containing the food and cooking gear.After they have gone 15KM, they swap packs and discover that Jake's Original pack is twice as heavy. They transfer 6kf og food from Robyn's new pack to Jake's new pack, so that when they have completed the final 25KM, the total weight and distance will be the same for each person.Write an equation to find the original weight of each pack, then solve for the original weight.

Any idea on how to do this? I keep getting stuck on the wording, am not sure if its just me not understanding
 
Robyn and Jake go on a hiking trip. Robyn starts off carrying the pack with the tend and sleeping bags, and Jake stars with the one containing the food and cooking gear.After they have gone 15KM, they swap packs and discover that Jake's Original pack is twice as heavy. They transfer 6 kf og food from Robyn's new pack to Jake's new pack, so that when they have completed the final 25KM, the total weight and distance will be the same for each person.Write an equation to find the original weight of each pack, then solve for the original weight.

Any idea on how to do this? I keep getting stuck on the wording, am not sure if its just me not understanding

We have lots of ideas - what are yours??!

To start off

What do we need to calculate ? Assign a variable name to each o the unknowns(to be calculated)

Original weight of Jake's pack = J (I am not sure the unit you are supposed to use - kf og is not a known unit to me)

Original weight of Roby's pack = R

Now continue.....

Duplicate Post:

http://openstudy.com/updates/54c8c9eae4b00b5402c3e57e
 
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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 "kfrog", a unit equal to the weight of a thousand frogs!:p

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"?)
 
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