Sunday Times Teaser 2889 – Catching the Bus

by Michael Fletcher

Published February 4 2018 (link)

I can travel to town by either the number 12 bus or the number 15 bus. The number 12 bus leaves every 12 minutes and the number 15 bus leaves every 15 minutes. The first number 15 bus leaves soon after the first number 12 bus. I arrive at the bus stop at random and catch the first bus to arrive.

If the probability of me catching the number 15 bus is 2/5 how soon does the first number 15 bus leave after the first number 12 bus?