Thomas is a big fan of motocross racing. Riders often complete 20 or more laps that are 500 m (3 miles) to two km (1.24 miles) long. This time, a friend who is also a fan of lap racing accompanies him. During the warm-up, Thomas points to one of the riders and says: "There is my favorite rider, Freeman—the man on the red motorcycle." "Yes, I see him," his friend replies and asks: "How many riders actually take part in the race”? Thomas answers with a smile: "One fifth of the drivers in front of Freeman add up to five sixths of the drivers behind him.”
How many drivers are in the race?
First of all, it is important to recognize that the information on the number of laps and the length of the track are irrelevant. On a circuit, the same number of riders are behind you as in front of you if you disregard their placement—like in the warm-up.
For x, the total number of drivers, you get the following formula:
1/5 (x - 1) + 5/6 (x - 1) = x | * 30
6x - 6 + 25x - 25 = 30x
31x - 31 = 30x | -30x
x = 31
So, 31 drivers, including Freeman, are participating in the race.