Last week I travelled from London to Leeds, which is a distance of 174 miles.
I started at 9.15am and completed the journey with an average speed of 40 miles per hour.
On the way back, in the evening, I travelled exactly the same route, starting at 5.15pm. The traffic was light and I completed the journey with an average speed of 60 miles per hour.
What was the overall average speed for round trip?
The answer is not 50 mph.
[Ref: ZTAH] © Kevin Stone
Direct Link: www.brainbashers.com?ZTAH
Hint: Remember that Time = Distance ÷ Speed, and Speed = Distance ÷ Time.
48 miles per hour.
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.
4 shepherds were watching over their flocks and they were commenting on how many sheep they each had.
If Alex had three more sheep, then they'd have one less sheep than Blake.
Whereas Drew has the same number as the other three shepherds put together.
If Charlie had three less sheep, they'd have exactly treble the number of Alex.
If they were evenly distributed they'd each have eleven sheep.
How man sheep does Alex have?
[Ref: ZIZG] © Kevin Stone
Direct Link: www.brainbashers.com?ZIZG
Hint: Find how many sheep Drew has first.
If we denote Alex by A, Blake by B, Charlie by C and Drew by D we can find the answer in the following way.
Since A + B + C = D and A + B + C + D = 44, it is easy to see that D has 22 sheep.
So A + B + C = 22.
We can use this along with the two other facts, A + 3 = B - 1 and C - 3 = 3A, to find that A has 3, B has 7, C has 12 and D has 22.
In a little more detail:
A + B + C = 22 (1)
A + 3 = B - 1 (2)
C - 3 = 3A (3)
Rearrange (3) to give C = 3A + 3 and replace the C in (1) to give A + B + 3A + 3 = 22.
Simplified this gives B = 19 - 4A (4).
Rearrange (2) to give B - A = 4.
Use (4) in the place of B to give 19 - 4A - A = 4 to give A = 3.
Now use A to work out B, and then C.
Move from letter to letter and collect the necessary letters for FIND (in any order).
How many different routes can you take if you always start with the central F and always move either horizontally or vertically?
N I D
D N D I D
D I N F I I N
I N D D I
D I D
[Ref: ZMHZ] © Kevin Stone
Direct Link: www.brainbashers.com?ZMHZ
Hint: You can't move diagonally.
Answer: 5 ways.
Starting at the central F, you can go:
Up, Up, Left.
Left, Left, Left.
Left, Left, Up.
Down, Left, Left.
Down, Down, Down.
Last week, I travelled from London to Stoke.
On the first day I travelled one half of the distance.
On day two, I travelled one third of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one half of the remaining distance.
I now have 5 miles left to travel.
How far is it from Stoke to London in total?
[Ref: ZRBH] © Kevin Stone
Direct Link: www.brainbashers.com?ZRBH
Hint: Try working backwards.
Answer: 120 miles.
On the first day I travelled 60 miles, leaving 60 miles. On day two I travelled 20 miles, leaving 40 miles On day three I travelled 30 miles, leaving 10 miles. Yesterday I travelled 5 miles, leaving 5 miles.