Problem K. 350. (November 2012)

K. 350. Steve lives far away from his new workplace, so he decided to go to work by car. On the first day, he travelled at an average speed of 70 km/h (practically uniformly), and arrived 1 minute late. On the second day, he started out at the same time but travelled at an average speed of 75 km/h (practically uniformly) and arrived 1 minute early. How far does he live from his workplace?

(6 pont)

Deadline expired on December 10, 2012.

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

Megoldás. Ha Pisti \(\displaystyle x\) óra alatt ért be az első nap a munkahelyére, akkor másnap \(\displaystyle 2/60\) órával korábban. A megtett távolságok megegyeztek, tehát \(\displaystyle 70x=75\left(x-\frac{2}{60}\right)\), rendezve \(\displaystyle x=\frac12\). Tehát Pisti \(\displaystyle 70\cdot\frac12=35\) km-re lakik a munkahelyétől.

Statistics:

181 students sent a solution.
6 points:	128 students.
5 points:	16 students.
4 points:	13 students.
3 points:	10 students.
2 points:	6 students.
0 point:	8 students.

Problems in Mathematics of KöMaL, November 2012