Alice and Bob are running a marathon (26.2 miles). Alice runs at a constant speed and covers one mile every 8 minutes. Bob runs at a variable speed, but runs every mile in exactly 8 minutes and 1 second. (i.e. no matter where he is on the track, he will be one mile farther in exactly 8 minutes 1 second.) Is it possible for Bob to finish the marathon faster than Alice?
Name:
Anonymous2009-01-22 17:00
Yes.
Name:
Anonymous2009-01-22 19:39
Obviously, shitty problem.
Alice reaches 26 miles in 208 minutes.
Bob reaches 26 miles in 208 minutes and 26 seconds.
Now alice will finish in 208 minutes and 8/5 minutes, so she won't finish before 209 minutes.
However Bob can run the last .2 miles in whatever time he pleases.
Name:
Anonymous2009-01-22 21:16
But if he speeds up like fuck at the 26 mile mark, how do you know he won't run the 25.1-26.1 mile in less than 8.1 minutes?
>>4
He can run the first mile however he wants (taking 8:01) and then he'll have to repeat that exact pattern for all the following miles. So Eve knows who will finish first when Bob reaches ~322 metres (or maybe 370 metres, or something else entirely).