After visiting one of my very old relatives, I travelled home in their old jalopy. The car was old and battered, it had a leak from the petrol tank, and I was stuck in second gear.
This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel.
At the start of the journey, I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour.
Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.
How far was it from my relative's house to my home?
Hint
You might find Pythagoras' theorem very useful [a2 + b2 = c2].
Answer
148 inches.
We can use Pythagoras' theorem if we draw an imaginary line across to create a right-angled triangle.
The hypotenuse is equal to the rope's length R. The bottom of the triangle is 48 inches. The vertical side is R − 8 (the difference between 20 inches and 12 inches).
Pythagoras' theorem tells us that:
a2 + b2 = c2
Where c is the hypotenuse.
This gives us:
482 + (R − 8)2 = R2
2304 + (R − 8)(R − 8) = R2
2304 + R2 − 16R + 64 = R2
2304 − 16R + 64 = 0
16R = 2368
R = 148
As required.
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Puzzle 363
Place letters into the grid such that every row, column, and 2 x 2 block has letters (in any order) that form a common word. Each letter is only used once, and no letter is repeated in the rows / cols / blocks.
Letters allowed: C O L U M B U S
D
K
P
E
T
E
L
A
Note: this puzzle is not interactive, and the squares cannot be clicked.
Other anagrams of these words are OK as long as they don't change the answer grid.
Alternative Answer
This answer uses less common words.
D
U
C
K
S
P
U
L
O
M
E
T
E
L
B
A
Across: DUCK, PLUS, TOME, BALE
Down : DOSE, PLUM, CUBE, TALK
Boxes : SPUD, LUCK, MOLE, BEAT
Other anagrams of these words are OK as long as they don't change the answer grid.
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Puzzle 364
Starting with the 6 in the bottom left corner, what is the highest total you can make, if you only move up or right, using the mathematical signs on the way?
+
4
−
1
+
3
2
+
4
−
1
+
−
3
+
2
−
2
2
−
4
+
3
−
+
3
−
1
+
2
6
+
1
−
2
+
Note: this puzzle is not interactive, and the numbers cannot be clicked.
