Random Puzzles 

Workings

Hint
The country spans more than one word.

Answer
England.

Alex's aches and pains felt worse because of swollEN GLANDs that had flared up during the night, perhaps a tonic would help?

Workings

Hint
What do the 3 numbers add to, and multiply to, so far?

Answer
$0.50.

Reasoning
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.

The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.

You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.

The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P

    8.50 + P = 18.00 x P

        8.50 = 18.00 x P – P

        8.50 = 17.00 x P

8.50 ÷ 17.00 = P

           P = 0.50.

Workings

Hint
It doesn't matter how far it was to Manchester, so you can use any distance.

Answer
Billie.

Reasoning
If we call the one way distance T, we know that:

On the way there, Alex drove 90 miles, and Billie drove (T – 90) miles.

On the way back, Alex drove (T – 100) miles, and Billie drove 100 miles.

So, in total, both ways:

   Alex drove 90 + (T – 100)
      = T – 10

   Billie drove (T – 90) + 100
      = T + 10

Therefore, Billie drove 20 miles more than Alex.

Workings

Hint
There are 60 seconds in a minute, and 60 minutes in an hour.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 60 x 24 x 365 = 525,600 minutes in a (non-leap) year.