On Dynamos nobody stands still: houses glide along rails, streetlights swing like pendulums, and the traffic lights go jogging. Kinesys has barely landed when a conveyor belt drags it away and dumps it at a highway toll booth.
“If we have to keep moving, at least I’m driving,” says Liz, and she rents a space car. Dord sits in the back, stiff as a board, checking the speedometer every two seconds. M00N, at the window, cheerfully waves at every truck they pass and counts them out loud.
After half an hour on the road, M00N proudly announces the total. Dord frowns: “Interesting. From that number, we can work out how many trucks go through here every hour.”
The Riddle
Driving along a stretch of highway at a constant 70 mph, a driver passes, in 30 minutes, 40 trucks that are themselves traveling at 50 mph.
Assuming all speeds are constant and, above all, that the traffic flow is constant, how many trucks travel along that highway in one hour? In short: how many trucks would a hypothetical person standing by the side of the road (a very rare sight on Dynamos) see go by in one hour?
Hint
Look at it from the trucks’ point of view: how fast is the driver passing them? From there you can work out how far apart two consecutive trucks are.
Solution
The answer is 200 trucks an hour.
Relative to the trucks, the driver is moving at 70 − 50 = 20 mph. So in half an hour she covers 10 miles relative to the trucks. That means a 10-mile stretch of road holds 40 trucks, so each truck is 10 miles / 40 = 0.25 miles (a quarter mile) from the next one.
For someone standing by the side of the road, the time between one truck and the next is 0.25 miles / 50 mph = 0.005 hours, or 18 seconds. So in one hour, 3,600 / 18 = 200 go by.