Minus' Solution to
Posted Weeks of May 4 - 17, 1998
Minus' Solution to
If you like working with fractions, then you probably enjoyed this questions. Here's why:
First bounce 40 + 40 = 80
Second bounce 40 + 40/2 = 60
Third bounce 40/2 + 40/3 = 33 1/3
Fourth bounce 40/3 + 40/4 = 23 1/3
Fifth bounce 40/4 + 40/5 = 18
Sixth bounce 40/5 + 40/6 = 14 2/3
Seventh bounce 40/6 + 40/7 = 6 2/3 + 5 5/7
Eighth bounce 40/7 + 40/8 = 5 5/7 + 5
Ninth bounce 40/8 + 40/9 = 5 + 4 4/9
Tenth bounce 40/9 + 40/10 = 4 4/9 + 4
In total: 266 + 6/3 + 10/7 + 8/9
= 268 + 146/63
= 270 20/63
~ 270.32
From Taryn Chua, of Methodist Ladies' College, must have read Minus' mind. She whipped-up a solution that was exactly what our mascot craved. Besides which...Minus really liked being called Mister.
Dear Mr. Minus-Shark, Bounce 1 = 1/1(40) = 40m dropped 40m, bounced 40m Bounce 2 = 1/2(40) = 20m dropped 40m, bounced 20m Bounce 3 = 1/3(40) = 13 1/3m dropped 20m, bounced 13 1/3m Bounce 4 = 1/4(40) = 10m dropped 13 1/3m, bounced 10m Bounce 5 = 1/5(40) = 8m dropped 10m, bounced 8m Bounce 6 = 1/6(40) = 6 2/3m dropped 8m, bounced 6 2/3m Bounce 7 = 1/7(40) = 5 5/7m dropped 6 2/3m, bounced 5 5/7m Bounce 8 = 1/8(40) = 5m dropped 5 5/7m, bounced 5m Bounce 9 = 1/9(40) = 4 4/9m dropped 5m, bounced 4 4/9m Bounce 10 = 1/10(40) = 4m dropped 4 4/9m, bounced 4m Total Distance travelled = 3(40) + 2(20) + 2(13 1/3) + 2(10) + 2(8) + 2(6 2/3) + 2(5 5/7) +2(5) + 2(4 4/9) + 4 Total Distance travelled = 270 20/63m So the answer is 270 20/63m, disregarding winds, gravitational forces, flying birds, pedestrians, potholes and flying saucers.
Verni Sundararajan knows how to manipulate fractions in a series. This delightfully short, but most succulent dish is proof. Bravo, Verni, for showing us how to do it right!
This is my solution: 40 + 40 X 2 (1/1 + 1/2 + 1/3 + ... + 1/9) + 40/10 = 40 + 80 X 2.8289683 + 4 = 44 + 226.32 = 270.32 metres The ball bounced approximately 270.32 metres.
Breena Blevins, Megan Marshall, and Megan Monday, from Pulaski Middle School, tempted Minus with an answer. No style marks, but four stars for effort.
If the problem was that the ball kept bouncing, the answer should be 270 20/63 meters.
Alice Beale & Jennifer Fontein also came close. A small rounding error might have led to a slight deviation from the norm.
Xerxes' ball bounced very strangely. This is how far we think the ball bounced: 270.2727272
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