Ben and Landon took turns driving on their recent 820 mile road trip. Ben averaged 60 miles per hour while landon averaged 56 miles per hour. If the trip took them 14 hours, how many hours did landon drive? cv cx

Landon drove for 5 hours.

Step-by-step explanation:

Given that,

Total distance of the road trip = 820 miles

Speed of Ben = 60 miles per hour

Speed of Landon = 56 miles per hour

Step 1:

Let 'x' be the number of miles Ben drove

Let 'y' be the number of miles Landon drove

Step 2:

The trip took them 14 hours to complete 820 miles together.

x + y = 14

60x + 56y = 820

Step 3:

Solve the linear system x + y = 14 and 60x + 56y = 820

x + y = 14

x = 14 - y

Step 4:

Substitute x = 14-y in the second equation,

60 (14-y) + 56y = 820

840 - 60y + 56y = 820

Step 5:

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.