perplexus.info :: Just Math : Tom and Harry Run to School

Tom and Harry Run to School (Posted on 2009-05-20)

Tom and his brother Harry had a foot race from their home to school, which was an integral number of yards away. Harry ran faster than Tom, but less than twice as fast, and arrived at the school when Tom was still a 2-digit integer of yards behind.

The next day they ran the race again, but this time Harry started farther away from the school by the same amount as the winning margin the previous day, while Tom still started the same time as Harry, but again from home. Of course, since Harry still runs faster, the same ratio as the day before, he finished the difference in distances in less time than it would have taken Tom, but this time the gap at the end was reduced so that when Harry reached school, the amount by which Tom was behind had the two digits reversed from the preceding day.

How far was it from their home to school, and what was their gap at the end of each run when Harry arrived at school?

Submitted by Charlie

Rating: 4.0000 (2 votes)

Solution: (Hide)

The distance between home and school was 192 yards. Tom was 72 yards short of school the first day when Harry had finished the run, indicating Tom was only 5/8 as fast as Harry. The second day, with the 72-yard handicap, Harry beat Tom by only 27 yards.

list 10 for D=20 to 1000 20 RestMax=int(D/2) 30 if RestMax=D/2 then RestMax=RestMax-1 40 if RestMax>99 then RestMax=99 50 for Rest=10 to RestMax 60 RVel=(D-Rest)//D 70 NewRest=D-(D+Rest)*RVel 80 if NewRest=int(NewRest) and NewRest>10 and NewRest<100 then 90 :Rev1=Rest\10+10*(Rest@10) 100 :if Rev1=NewRest then print D;Rest,RVel,NewRest 110 next Rest 120 next D OK run 192 72 5//8 27 OK Based on Enigma No. 1534, "Head start", by Susan Denham, New Scientist, 28 February 2009, page 24.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	williamwill009	2024-01-19 04:43:25
Puzzle Answer	K Sengupta	2023-12-20 02:02:29
write a competent essay	David	2023-12-19 16:12:23
No Subject	CodyDunning	2023-11-24 05:37:33
Preschool	CodyDunning	2023-11-14 07:33:40
Puzzle Thoughts	K Sengupta	2023-08-15 09:01:18
re: Education	watson1	2023-08-14 14:57:50
Education	Ruby Coupp	2022-10-15 03:13:26
No Subject	JamesYawn	2022-04-11 04:35:56
School Education	Dylan McGregor	2022-01-17 05:04:29
Education	MaxDelaney	2022-01-13 11:27:18
Education	Hayden Franki	2021-11-23 09:08:39
Solution	Dej Mar	2009-05-26 17:16:54
analytic solution	Daniel	2009-05-20 12:12:17

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