Formula needed

[Crispy10]

I recently had to take a "Critical Thinking" test during a job interview. One of the questions I couldn't get was something similar to this:

A shaft is sticking out of the water 7'
1/2 of the shaft is buried in the ground
1/3 of the shaft is in the water

What is the total length of the shaft?

Any input to this question would be greatly appreciated.

Thank You

 

[kmcandy14]

Wait, wouldn't that mean that it's just 14''? Since half of it is in the ground, and 7'' are in the air? Or am I missing something? What was the correct answer? Did they tell you?

Again, sorry this was so late!!

 

[Country Boy]

No, 7 inches are in the ground and 7 inches are in the air but there may be an unstated length in water between the ground and the air.

Half of the shaft is in the ground and one third of the shaft is in the water. Let "X" be the length of the whole shaft in inches. X/3 is in the ground, X/2 is in the water, and 7 inches were in the air. Altogether X= X/3+ X/2+ 7. Can you solve that for X? (Since I don't like fractions I would start by multiply both side by 2*3= 6.)

 

[Country Boy]

Since this has been here a while, (first posted in 2016, my response was earlier this month) I am going to complete the solution.

We have x= x/2+ x/3+ 7. Multiply by 6:
6x= 3x+ 2x+ 42. x= 42. This shaft is 42 inches long.

Check: 1/2 of the shaft is 42/2= 21 inches. 1/3 of the shaft is 42/3= 14 inches. There are 21 inches of the shaft in the ground, 14 inches of the shaft in the water and 7 inches of the shaft in the air. That is a total of 21+ 14+ 7= 42 inches as required.