Quandaries
and Queries 

A train with 2 cars is traveling at a speed of 80 km/hr from town X to town y, located 800 km from each other. At the same moment that the train departed, a passenger started to walk back and forth from one end of car B to the other at a speed of 100cm/sec. Arriving in town Y, the passenger had already gone and returned 720 times. The length of car A is that of car B plus one fourth of the length of the locomotive, and the length of the locomotive equals the length of Car A plus one fifth of the length of car B. What is the total length of the train? 

Hi Michael, There are three major steps to solve this problem. Step1: The train travels at 80 km/hr and travels 800 km, thus the train travelled for 10 hours. Step 2: The passenger walked at 100 cm/sec for 10 hours and thus walked
He walked the length of car B 7202=1440 times and hence car B is
Step 3: Let A designate the length of car A and L designate the length of the locomotive. You now have two facts. The first is "The length of car A is that of car B plus one fourth of the length of the locomotive". That is
The second fact is "the length of the locomotive equals the length of Car A plus one fifth of the length of car B" Write this second fact as an equation and then solve the two equations for A and L. Cheers, Penny 

