Ben and Landon took turns driving on a 820 mile road trip. Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. The trip took them 14 hours. How many hours did Landon drive?

Answer:

See below!

Explanation:

equation for distance:

Lets Ben hours be x and Landon hours be y,

60x + 56y = 820 .........equation 1

equation for time:

x + y = 14 .........equation 2

Make x the subject:

60x + 56y = 820

x = (820 - 56y)/60 ..........equation 3

x + y = 14

x = 14 - y ........equation 4

Solve equation 3 and 4 simultaneously:

             [ Therefore Landon drove 5 hours ]

Extra's further investigated:

if y = 5

              [ Therefore Ben drove 9 hours ]

you can't solve x because it is 2 linear equation and you only have one equation