how many miles a day

Question

The Natchez Trace Parkway is a historical 444-mile route from Natchez, Mississippi, to Nashville, Tennessee. A couple drove the Trace in four days. Each day they drove 8 miles more than the previous day. How many miles did they drive each day?

Answer 1

Hi Katelyn,

 

There are many different ways to approach this problem. Let's reason it out first without starting with an equation. 

 

Each day they increase the mileage by 8 miles, so on day 2 they do 8 miles more, and on day 3 16 miles more, and on day 4 24 miles more.

 

 If we total the extra mileage up we get 8 + 16 + 24 = 48 extra miles.  

 

If we subtract the extra miles from the 444 toral miles,  we get 396 miles.  If we divide that by the 4 days we get the base miles of 99 miles per day.

 

To summarize, they travel 99 miles on day 1, 107 miles on day 2, 115 miles on day 3, and 123 miles on day 4.

 

If we check our work

 

 99 + 107 + 115 + 123 = 444 miles.

 

You can use the same logic to convert the thought process above into an algebraic equation.  If you have any questions,  ask away. 

 

Sincerely, 

 

Ralph K. 

Answer 2

Suppose they drove x miles the first day.

 

The next day they drove x + 8, and the two days after that x + 16 and x + 24.

 

So the total they drove was x + (x + 8) + (x + 16) + (x + 24) = 4x + 48.  Since that's 444 miles, that gives us an equation:

 

4x + 48 = 444

4x = 396

x = 99

 

So the first day they drove 99, followed by 107, 115, and 123 on the next three days.