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

100cm/sec60sec/min60min/hr10hr = 3600000cm
which is 36000 meters

He walked the length of car B 7202=1440 times and hence car B is

36000/1440 = 25 meters long

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

A = 25+¹/₄L

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

Go to Math Central