Mathematical Puzzles 

Workings

Hint
It doesn't matter what the distance is, so try a random distance.

Answer
This cannot be done.

It does not matter how far the trip is, let's assume that it is random distance, say 60 miles, and remembering that Time = Distance ÷ Speed.

The morning trip took 60 miles ÷ 30 mph = 2 hours.

To average the required 60 mph, we would have to travel the total distance (of 120 miles) in 2 hours. However, we've already used all of the two hours for the morning trip!

Choosing any random distance would also show that it can't be done.

Workings

Hint
Try working backwards.

Answer
15.

Reasoning
One quarter of 360 is 90.

One third of 90 is 30.

One half of 30 is 15.

Workings

Hint
How much petrol was used for the journey itself?

Answer
3 gallons each hour.

Reasoning
I drove 300 miles at 30 miles per gallon, so I used 10 gallons. Which means I lost the other 15 gallons.

I drove the 300 miles at 60mph, which took me 5 hours.

So I lost 15 gallons of petrol in 5 hours = 3 gallons per hour.

Workings

Hint
How many minutes are between the times?

Answer
50 minutes.

Reasoning
If we call the number of unknown minutes T.

Between four o'clock and eight o'clock, there are 240 minutes.

There is some point between these two times, before which we have 3 lots of T, and after which we have one lot of T plus 40 minutes.

Therefore, in the 240 minutes, there are 4 lots of T plus 40 minutes.

   240 = 4 x T + 40.

Therefore, T = 50 minutes.