Enigma 1070: Time to work
19 March 2018
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From New Scientist #2226, 19th February 2000 [link]
Amber cycles a distance of 8 miles to work each day, but she never leaves home before 0730h. She has found that if she sets off at x minutes before 0900h then the traffic is such that her average speed for the journey to work is (10 − x/10) miles per hour. On the other hand, if she sets off at x minutes after 0900h then her average speed is (10 + x/10) miles per hour.
(1) Find the time, to the nearest second, when Amber should set off in order to arrive at work at the earliest possible time.
Matthew lives in another town but he also cycles to work, setting off after 0730h, and he has found that his average speed for the journey to work follows exactly the same pattern as Amber’s. He has calculated that if he sets off at 0920h then he arrives at work earlier than if he sets off at any other time.
(2) How far does Matthew cycle to work?