Puzzle 29
During a recent BrainBashers race meeting, the fastest driver managed to complete a lap with an average speed of 150 mph.
They managed to complete the first two fifths of the lap at a speed of 123 mph and the second two fifths of the lap at a speed of 164 mph.
At what speed was the final one fifth of the lap length covered?
The answer is not 176 mph.
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/ztxp
Hint
Adding the speeds won't work.
Answer
205 mph.
Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.
The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) x L] ÷ 123 hours.
The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) x L] ÷ 164 hours.
The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) x L] ÷ y hours.
The entire trip is covered at an average of 150 mph, and we can conclude that:
2L 2L L L
————— + ————— + ——— = ———
5x123 5x164 5y 150
Rearranging and simplifying gives:
1 1 2 2
——— = —— - ——— - ———
y 30 123 164
That means that y = 1 ÷ (1/30 - 2/123 - 2/164)
Using a calculator gives y = 205.
Puzzle 30
What are the next five letters in this sequence:
JAJWUTH
TFAPOW
JFDABHC
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/zvib
Hint
This is a well known nursery rhyme.
Answer
AJCTA.
These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.
Puzzle 31
Can you decode the following well known quote?
B DBBCC, DBADABCDA B AC
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/zoyc
Hint
The code has just four letters, A, B, C, and D. Each letter encodes 5 different letters.
Answer
I think, therefore I am.
Reasoning
A represents a, b, c, d, and e.
B represents f, g, h, i, and j.
C represents k, l, m, n, and o.
D represents p, q, r, s, and t.
E represents u, v, w, x, and y.
Puzzle 32
What letter comes next in this sequence:
A O E A O T F {?}
workings
hint
answer
print
Share link: https://www.brainbashers.com/puzzle/zlfx
Hint
This is quite a common alphabet.
Answer
L.
The last letter from hoteL, which is H in the phonetic alphabet, alphA, bravO, charliE, etc.
< previous next >
Note: BrainBashers has a Dark Mode option. For BrainBashers, I'd recommend not using your browser's built-in dark mode, or any dark mode extensions (sometimes you can add an exception for a specific website).
