It sounds like one of those bizarre questions you might get at an Oxbridge interview: how can you despatch a letter 50 miles in one hour? Oh, and you are Lord March, the last Duke of Queensberry, later known as Old Q (his rapping name perhaps) and the year is somewhere around 1750. No Postman Pat little red van to help.
Lord March was an incredibly successful gambler, principally on the newly fashionable horse races at Newmarket. His talent lay in his scientific approach to horse racing and his creativity - sometimes manifesting as ingenious solutions to problems like the one above but more often as cheating. I read about him in 'Can we have our balls back, please?' by Julian Norridge, a great book about how the British gave sport to the world and let the world beat them at it. To quote from the book, 'throughout [March]'s life he is said to have won nearly a quarter of a million pounds. He had his best year at Newmarket when he was 63 and then retired to his house in Piccadilly to devote himself to his other great passion, the lusts of the flesh.'
So how did he win this bet? He enclosed the letter in a cricket ball, hired 24 of the best fielders of the time, stood them in a circle and instructed them to throw the ball around. The solution is extremely neat, but those fielders must have been bloody good: 50 miles in one hour equates to 1467 yards per minute and if the fielders stood fifty yards apart, they'd have to have completed their catch and throw (reaching the next fielder) in about two seconds. Seventy yards apart and they'd have around three seconds.
The more I think about it, the less plausible it seems, but why let that get in the way of a good story? It reminds me of another bet I heard of: A bets B he can throw a cricket ball 30 yards, make it stop and come back to him. B accepts the bet and watch A throw the ball 30 yards vertically into the air and catch it. D'oh.