Question 6
An engine is tested as follows. On the first road segment, the car travels at speed $v$. The second segment is twice as long as the first and is travelled at speed $2v$. The third is three times as long as the first and is travelled at speed $3v$. The car continues in this way: the $n$th segment is $n$ times as long as the first and is travelled at speed $nv$. Find $n$ so that the average speed over all the segments is $7$ times the average speed on the first segment. The speed is constant on each segment.