Mathematical and Physical Journal
for High Schools
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Problem K. 241. (February 2010)

K. 241. The road from village A to village B is divided into three parts. If the first section were 1.5 times as long and the second one were 2/3 as long as they are now, then the three parts would be all equal in length. What fraction of the total length of the road is the third section?

(6 pont)

Deadline expired on March 10, 2010.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Osszuk fel a harmadik útszakaszt hat egyforma részre, egy ilyen rész hossza legyen x. Az első útszakasz hosszának 1,5-szerese a 6x, tehát az első útszakasz hossza 4x. A második útszakasz hosszának 2/3 része 6x, tehát a második útszakasz hossza 9x. A teljes út tehát 4x+9x+6x=19x, így a harmadik útszakasz a teljes út 6/19 része.


162 students sent a solution.
6 points:63 students.
5 points:5 students.
4 points:2 students.
3 points:2 students.
2 points:67 students.
1 point:4 students.
0 point:18 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, February 2010