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:

distance = speed * timespeed = distance/timetime = distance/speed

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:

14 - y =  (820 - 56y)/6060(14 - y) = 820 - 56y840 - 60y = 820 -56y840 - 820 = -56y + 60y20 = 4yy = 5

             [ Therefore Landon drove 5 hours ]

Extra's further investigated:

if y = 5

x = 14 - yx = 14 - 5x = 9

              [ Therefore Ben drove 9 hours ]