Math Puzzle: Hunting Deer
Two hunters killed a deer and sold it by the pound in the woods. They had no proper means of weighing it, but knew their own weights-one 130 pounds and the other 190 pounds. They placed a rail across a fence so that it balanced with one of them on each end. They then exchanged places, the lighter man taking the deer in his lap, and the rail again balanced. What was the weight of the deer?
If you can figure this out, answers can be entered in the ‘comment’ section below. Will reveal Thursday.
147.692 lbs
147.69 lb
Hay there, Doc.:
I could see other people’s comments before they are moderated.
Look at this!:
Math Puzzle: Hunting Deer
brianu | Profile (beta) March 16th, 2010 – 12:52 am says
147.692 lbs
Moment is force x distance, so I plugged in an arbitrary distance for the dad (A), and calculated how far away the son must be sitting (B). I then reversed their positions, added the weight of the deer (D) to the son’s side, and solved for D.
1. 190*A = 130*B
2. (130+D)*A = 190*B
3. D = 147.69 pounds
About 147.7 pounds.
Now thay are gone!!
I could only see my comments.
thnx.
For the board to balance, length*weight must be the same on both sides.
Writing the weights in parentheses, the first balance looks like this:
190(130) = 130(190)
Keeping the same lengths, but with the new weights, the new balance is:
190(190) = 130(130+D)
Solving this gives a weight of 147.69 lb for the deer.
At first, the two hunters weight was balanced
130=190
Since this could not be true, the rail must not be placed in the center, therefore a certain weight of the longer length of the rail in comparison to the shorter side is added to the lighter hunter (130)
130+60=190
The rail is 60 pounds heavier on the left side.
The two hunters switched place, so the weight of the longer part of the rail (60), on the left is added now to the heavier man who is now on the left also (190)and the deer is taken by the lighter man(130)
190+60 = 130+ Deer
250 = 130 + Deer
250 – 130 = Deer
120 = Deer
The Deer is 120 pounds.
I think the answer is 147.69 pounds, the relationship between the weights is close to 1.47 to balance in case 1, so in case to with lighter man with the deer in his back, you multiply 190 with the factor and substract the other man weight 130 and you get the weight of the deer, cool.
Congratulations on the new site. Continuous improvement is always a good thing. It can only get better!
About a 148 lb deer in a 130 lb man’s lap balanced over a fence on a rail with a 190 lb man on the other end? This is a picture I’d like to see!
147.7 lbs.
The scale is weighted so that one side is about 46% heavier than the other.
190+(190*.46)-130=147.4 The 147.7 above is achieved without rounding to 46% even.
If ‘d’ is the weight of the deer in pounds, then:
(130 + d)/190 = 190/130
=> d = 147.69 pounds
Well using equilibrium of forces around a pivot and solving for simultaneous equations i got 147.69 pounds but I have been known to mess these up…
190/130 = (130+W)/190
W=147.692 lbs
RK, Some comments still under moderation are available in the recent comments section!
I see you took middle ground between releasing comments immediately and moderating them
Very good, 147.69 pounds.
@Hex- not intentional, I promise!!
Also on homepage- a direct link is now available for ‘Your Profile’. This will factor in a lot more with the quiz module which is actually almost finished.
What was the weight of the rail? (assuming that it was uniform)
The answers so far appear to assume the rail has no weight (which is what the textbooks do). In real life if the rail were centered then the force from the weight of the rail on each side would cancel and you could make the assumption that the extra weight applied to each side is equal. Thus balance beams work in real life as long as they balance when zeroed
However in real life with the rail off center the weight of the rail itself will introduce unbalanced force on the longer side which the suspended weight on the shorter side will need to compensate for. When sides are switched then the force must be made up by other object.
I think the deer will weigh less then 147.69 lb answer from a zero weight rail. The heavier the rail the less the dear would weigh. As rail weight increased even futher it would seem that at some point when they switched side the 130 lb hunter plus dear could’nt get the other side of the rail off the ground.
Sooo… was this a super dry 2×4, a pressure treated 4×4, a railroad tie or 20′ concrete pier?
Maybe the problem here with the original question.
It states “so that it balanced with one of them on each end.” It’s the “end” part that causes the problem. This forces the beam to be off center and thus it not be in balance itself.
If this were changed to: “A beam if first positoned so it in balanced with no one on it. They then positioned themselves on the beam such that it is still in balance. Then exchanged places…”