Elementary POW, March 10-14, 1997


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A frog is at the bottom of a 30-foot well. Each day he climbs up 3 feet. Each night he slides down 2 feet. On what day will he reach the top of the well and escape? Make sure you explain how you arrived at your answer.

Bonus Puzzler

I came across an interesting "fun fact" in our school newspaper today and I'd like you to check it and determine if it is correct.

You're going to have to do some research to back your answer up with facts.

Dan Tobin of Germantown Academy, Fort Washington, PA looked over this week's submissions:
There were a lot of answers for this problem. The problem appeared to be a no-brainer at first, but some of the kids who read it more carefully and worked through it came to the correct solution of 28 days. Only a handful tried the bonus puzzler, so I wrote up everyone who attempted it. Many of the kids who researched it found that a cooked hamburger at a fast food restaurant would cost more pound for pound than a car. However, an uncooked hamburger at a supermarket usually costs less than a car, pound for pound.

Correct Solutions submitted by:

Highlighted Solutions

Stephanie Kolling
Mrs. Freeman's 5th grade
Stony Lane School
North Kingstown, RI

Hi! My name is Stephanie. My answer was the frog will reach the top of the well on the 28th day. I made a well with 30 rectangles to represent the 30 feet the frog has to climb. Then, I made a small mark to represent how far the frog climbed that day. Every day I would go up three spaces and climb down two. This is really like climbing up 1 foot each day. Then, when I climbed up three spaces on the 28th day, I was out of the well so I did not have to go down three spaces. I used the strategy make a picture. When I did this problem, I realized that it was harder than I thought. You would never think that after the 28th day you were out.

Vinay Aggarwal
Paul Nass
Fourth, 9 years old
Georgetown Day School, Wash. D.C.

My answer to this problem is on the 28th day the frog will escape from the well. I got this answer by making a chart. First I drew a rectangular box. Next to it I numbered the days. I estimated it would be 30 or so, so I numbered 1-30. I also made 30 lines in the box, 1 for every foot. Then I made lines in the box gowing up 3 and back down 2 for each day and night.

Bonus Puzzler Solutions

William Ewing
Bonner 3rd grade
Center school
Stow MA

A pound of hamburger costs $2.89 which can be rounded up to $3.00. A cheap car which weighs 2,000 pounds if it were three dollars a pound it would only cost $6,000 when most cars cost $14,999.99. Pound for pound hamburgers cost less than new cars is the correct answer.

Johannah Cornblatt
Paul Nass's 4th grade
Georgetown Day School
Washington D.C.

The answer to the bonus puzzler was no. The newspaper was wrong. I rounded and said that a hamburger costed a dollar per pound. I got the weight of a car. I found out how much the car cost and tried to find how many times the weight went into the price. I tried it with another weight of a car. The amount that the weight could go into the price was simply too much for a hamburger to cost.

Udit Garg
Grade 4
Paul Nass
Georgetown Day School
Washington D.C.

Hamburgers do cost more than new cars Facts: My TOYOTA CAMRY weighs 4,000 pounds and new cars cost at a average $20,000.00 so I did the math and that makes it $5.00 per pound. At McDonalds their quarter-pounder costs $2.19 and I multiplied it by 4 and the answer was $8.72.

Heather Comerci, Andrew Dang, Sam Henderson, Gordon Faylor
grade 5
Western Salisbury School (Mrs. Geschel)
Allentown, PA

We wrote to some car sites on the internet and got prices and weights for various cars. We figured out the average weights and average costs,and then we divided the cost by the weight and got approximately $5.50 a pound for the cars.

We priced hamburgers at local fast food restaurants, and the average cost of a quarter pound hamburger was $2.25. Then we multiplied by 4 (for a WHOLE pound), and it came out to $9.00 for a pound of hamburger. We also priced hamburger meat from some local grocery stores. We would pay an average of $2.00 a pound if we got it there. SO... it depends which kind of a hamburger you're comparing cars to.

ALSO one of our responses from someone on the internet told the price of a FerrariF60 (2712 lbs.) for $487,000. If we'd figured that into our averages, the cars would definitely be more expensive

Katherine Yang
third
Mrs. Sponenburg
Holmdel Village School
Holmdel, New Jersey

A quarter-pound burger would cost $2.50. So a burger that weighed a pound would cost $10. A car would cost $18,000. A car would weigh 3,000 pounds. A pound of a car would worth $6. 

          CAR     BURGER
          3,000   3,000
          x $6    x $10
          ------- -------
          $18,000 $30,000

Vinay Aggarwal
Paul Nass
Fourth, 9 years old
Georgetown Day School, Wash. D.C.

I figured out this problem by getting information. I looked in a car magazine with many weights and prices of cars. I picked the Toyota Camry. Then I got information on Roy Rogers hamburgers. I got the weight and price. Then after doing some math I determined that the "fun fact" was correct. Here are my calculations. 

Roy Rogers Hamburgers:      Toyota Camry: weight of car 3230 lbs, 
cost of 1/4 lb = $2.39      cost = $24,480 =
cost per pound = $2.39*4    cost per pound = $24,480/3230 =
burger = $9.56 per pound    car per pound = $7.58 per pound
The burger costs more per pound.

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