Random Puzzles 

Workings

Hint
If we look at all of the clues, each person appears exactly twice.

Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.

Reasoning
If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

   Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 − 22 = 21 years.

   Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 − 28 = 15 years.

   Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 − 36 = 7 years.

Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:

[1]   A + B = 36
[2]   C + B = 22
[3]   C + A = 28

If we use [3] − [2] we have:

[4]   A − B = 6

If we use [1] + [4] we have:

   2A = 42
    A = 21

By [1] B = 15. By [3] C = 7.

Workings

Hint
The country spans more than one word.

Answer
Chile.

At school, most of my friends learnt FrenCH. I LEarnt Chinese, mainly because I planned to visit the area when I grew up.

Workings

Hint
How far did I travel, and how much fuel did this use?

Answer
I had lost 4 gallons of fuel.

Reasoning
I travelled at 60mph for 4 hours, which is 240 miles.

At 40 miles per gallon this used 6 gallons, which meant the remaining 4 gallons were lost.

Workings

Hint
Could Alex have come first or second in any event?

Answer
   Vault  Beam   Floor
#1 Emery  Chris  Billie
#2 Chris  Billie Emery
#3 Alex   Emery  Chris
#4 Billie Alex   Alex

Reasoning
By (1), Chris came third on the floor. By (6), Billie came last in the vault.
   Vault  Beam   Floor
#1
#2
#3               Chris
#4 Billie

By (2), the athlete who came second in the vault won the beam event, let's mark these as X.
By (3), the athlete who came second on the beam won the floor, let's mark these as Y.
By (5), the athlete who won the vault came second on the floor, let's mark these as Z.
   Vault  Beam   Floor
#1  Z      X      Y
#2  X      Y      Z
#3               Chris
#4 Billie

By (4), Emery beat Alex in every event, therefore Alex can't have won any event, nor come second (because of X, Y, and Z). So, Alex came third on the vault, and last on the floor.
   Vault  Beam   Floor
#1  Z      X      Y
#2  X      Y      Z
#3 Alex          Chris
#4 Billie        Alex

Looking at the vault, Z can't be Chris because Z came second on the floor (but we know Chris came last). So, Z must be Emery, and X is Chris.
   Vault  Beam   Floor
#1 Emery  Chris   Y
#2 Chris   Y     Emery
#3 Alex          Chris
#4 Billie        Alex

Looking at the floor, Y is Billie.
   Vault  Beam   Floor
#1 Emery  Chris  Billie
#2 Chris  Billie Emery
#3 Alex          Chris
#4 Billie        Alex

By (4), Emery beat Alex on the beam.
   Vault  Beam   Floor
#1 Emery  Chris  Billie
#2 Chris  Billie Emery
#3 Alex   Emery  Chris
#4 Billie Alex   Alex