The Limited Times

Now you can see non-English news...

The Super Heavy Freight Train

2022-05-08T08:01:52.733Z


The train is 40 wagons long, three consecutive wagons always weigh 430 tons, and the total weight of the train is also known. How heavy are the two middle wagons?


Photo:

THE MIRROR

A freight train transports ore from the port of Hamburg to a steel works in Salzgitter.

The 40 wagons together weigh 5700 tons.

They are of different weight.

However, we know that three wagons hanging one behind the other always weigh exactly 430 tons.

What is the combined weight of the middle two wagons?

320 tons.

If the first three cars have the

masses a, b

and

c

, the fourth car must again have the mass a so that the mass of three consecutive cars does not change.

Wagon 5 therefore has mass b, wagon 6 has mass c and wagon 7 starts again with mass a.

The masses a, b, c follow one another again and again in this order – namely 13 times up to wagon 39. The first 39 wagons therefore weigh 13*430 = 5590 tons.

Wagon 40 again has the mass a.

Because the train weighs a total of 5700 tons,

a = 5700 - 5590 tons


a = 110 tons and

b + c = 430 tons - a


b + c = 320 tons.

The cars in the middle have the numbers 20 and 21. They therefore have the masses b and c.

Therefore 320 tons is the solution we are looking for.

I discovered this puzzle in the puzzle collection "Math with the Kangaroo 2019" of the student competition of the same name.

In case you missed a mystery from the past few weeks, here are the most recent episodes:

  • Magic with prime numbers

  • Strict logic in the rabbit hutch

  • You shall be many friends

  • Which number comes next?

  • The perfect seating arrangement for world explainers

  • Searched for sum of angles

  • Mysterious phone numbers

  • Looking for a cheap chain

  • How big is the blue area?

  • Get there quickly

Source: spiegel

All business articles on 2022-05-08

You may like

News/Politics 2024-03-01T10:24:37.181Z
News/Politics 2024-03-02T05:04:05.070Z

Trends 24h

Latest

© Communities 2019 - Privacy

The information on this site is from external sources that are not under our control.
The inclusion of any links does not necessarily imply a recommendation or endorse the views expressed within them.