In the given question, all the necessary information's are already provided. Using these information's it is easy to find the average speed of the car in miles per hour. It is given that the car covers 10 laps in 18 minutes and each lap is 3.6 miles in length.
Total distance covered by the car = (10 * 3.6) miles
= 36 miles
Now we have to convert the time from minutes to hours. So
18 minutes = 18/60 hours
= 3/10 hours
Now we can easily calculate the average speed of the favorite car of Mathew.
Average Speed = 36 * (10/3) miles/hour
= 120 miles/ hour
Translating into a mathematical equation:
n + n^2 = 72
Rewriting, n^2 + n - 72 = 0
Factoring, (n+9)(n-8) = 0
Solving for n: n = -9 or n = 8
You must check both answers before accepting one, the other or both.
Example: suppose we check out n = 8. Then 8 + 8^2 = 72 is true, and n = 8 is a solution. Is n = -9 a solution? Try it.
