Random Puzzles 

Workings

Hint
You don't need to use a calculator.

Answer
Cube root of 2.

Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy…

We have:

   10^1/₁₀ or 2^1/₃

Raise each to the power of 30 (since 10 x 3 = 30) to give:

   (10^1/₁₀)³⁰ or (2^1/₃)³⁰

   10^{1/₁₀ x 30} or 2^{1/₃ x 30}

   10³ or 2¹⁰

   1000 or 1024

Therefore, the cube root of 2 is larger.

Workings

Hint
Remember that Time = Distance ÷ Speed, and Speed = Distance ÷ Time.

Answer
48 miles per hour.

Reasoning
Using:
   Time  = Distance ÷ Speed
   Speed = Distance ÷ Time

The outward journey took 174 miles ÷ 40 mph = 4.35 hours.

The return journey took 174 miles ÷ 60 mph = 2.9 hours.

So I travelled a total of 2 x 174 = 348 miles. I did this in a total of 4.35 + 2.9 = 7.25 hours.

My overall average speed was therefore 348 miles ÷ 7.25 hours = 48 miles per hour.

Workings

Hints
The first letters of the words are: M, C, C, S, V, G, A, T, S, T, S, F, S, D, O.

Answers
---rix = matrix ---osy = choosy ---few = curfew ---oze = snooze ---uum = vacuum ---wth = growth ---nda = agenda ---nis = tennis ---tem = system ---pod = tripod ---reo = stereo ---hom = fathom ---gan = slogan ---amt = dreamt ---gen = oxygen

Workings

Hint
One of the words end in K. Remember that a skunk isn't a reptile, or an amphibian.

Answers
-r-g       = frog -o-t-i-e   = tortoise -n-k-      = snake -e-t       = newt -i-a-d     = lizard -r-c-d-l-  = crocodile -a-a-a-d-r = salamander -u-t-e     = turtle -k-n-      = skink a-l-g-t-r  = alligator