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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 5, September 2019

2019-09-15

## The Motocross Race

Figure out how many drivers are in the race!

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?

## Solution

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.

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