Landon drove for 5 hours.
<u>Step-by-step explanation</u>:
Given that,
Total distance of the road trip = 820 miles
Speed of Ben = 60 miles per hour
Speed of Landon = 56 miles per hour
<u><em>Step 1 </em></u><em>:</em>
Let 'x' be the number of miles Ben drove
Let 'y' be the number of miles Landon drove
<u><em>Step 2</em></u><em> :</em>
The trip took them 14 hours to complete 820 miles together.
x + y = 14
60x + 56y = 820
<u><em>Step 3 </em></u><em>:</em>
Solve the linear system x+ y= 14 and 60x+ 56y= 820
x + y = 14
x = 14 - y
<u><em>Step 4 </em></u><em>:</em>
Substitute x= 14-y in the second equation,
60(14-y) + 56y = 820
840 - 60y + 56y = 820
<u><em>Step 5</em></u><em> :</em>
Keeping y terms on one side and constants on other side,
60y - 56y = 840 - 820
4y = 20
y = 20/4
y = 5
Since 'y' is the number of miles Landon drove, the time Landon drove is 5 hours.
