An 18-year-old runner can complete a 10.0 km course with an average speed of 4.55 m/s. A 50-year-old runner can cover the same distance with an average speed of 4.05 m/s. How much later (in seconds) should the younger runner start in order to finish the the course at the same time as the older runner?

The young, fit, trim, strong, impervious, carefree runner's average speed is 0.5m/s faster than the average speed of the elderly, decrepit, infirm, dinosaur.

I thought that simple calculation was going to blow the whole solution wide open, but I can't see what to do with it, so I'll just use the obvious, old-fashioned, straightforward, brute-force method.

Time the whippersnapper takes to run the 10k = (10,000m) / (4.55m/s) = 2197.8 s.

Time the dinosaur takes to run the 10k = (10,000m) / (4.05m/s) = 2469.1

The codger needs 271.3 more seconds to stagger from the starting line to the finish line.

So if the youngster wants to rub it in, then he can sit down on the starting line for 271.3 seconds (4 minutes 31.3 seconds) AFTER the starter fires his pistol, then leap to his feet, and cross the finish line in a dead-tie with the oldster, after 41 minutes 9 seconds of running.