If the piece eaten on the fourth day weighed 12g, 96 grams did the whole cake weigh.
Solution
1/12 + 1/6 + 3/8 = 8/24 + 4/24 + 9/24 = 21/24

1 - 21/24 = 3/24

(3/24) * Whole Cake Weight = 12g

To find the whole cake weight:

Whole Cake Weight = 12g / (3/24) = 12g * (24/3) = 96g

Let's denote the length of the entire pole as "x" cm.
The remainder of the pole, which is not painted red, is (1 - 1/8) = 7/8 of the pole's length.

Now, we know that 2/7 of the remainder is blue. So, the length of the blue portion is (2/7) * (7/8) * x.

The remaining white portion is given as 150 cm.

Red length + Blue length + White length = Total length
(1/8) * x + (2/7) * (7/8) * x + 150 cm = x

To solve for x, we can simplify the equation:

(1/8) * x + (2/8) * x + 150 cm = x
[(1/8) + (2/8)] * x + 150 cm = x
(3/8) * x + 150 cm = x
3x + 1200 = 8x
1200 = 5x
x = 240 cm

Red length = (1/8) * x = (1/8) * 240 cm = 30 cm

Therefore, the length of the red portion is 30 cm.

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Solution:
3/10 + 3/20 + 1/12 = 8/15 is the total time length of his journey.