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 10 December 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 \(\displaystyle 70\cdot\frac12=35\) kmre lakik a munkahelyétől.
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