Solve without a calculator – 3

Relevant wiki: Lucas Numbers

This problem is very similar to the first problem in the set, but 29 isn't a Fibonacci number. Instead, it is a Lucas number; the ratio between consecutive Lucas numbers also tends to $\phi$ , so the answer is the next Lucas number, which is 47. $\beta_{\lceil \mid \rceil}$

1 mile = 1.609 km

$29$ miles $= (30 -1 )\times (1.609)$ nearly equals. $=(30 - 1) \times (1.61) = 48.3 - 1.61 = 46.69$

$ANSWER: [46.69] = \boxed{47}$