Question

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 1

Answer:

See below!

Explanation:

• distance = speed * time
• speed = distance/time
• time = distance/speed

equation for distance:

Lets Ben hours be x and Landon hours be y,

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

equation for time:

$\frac{60x}{60}+ \frac{56x}{56} =14$

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)/60
• 60(14 - y) = 820 - 56y
• 840 - 60y = 820 -56y
• 840 - 820 = -56y + 60y
• 20 = 4y
• y = 5

             [ Therefore Landon drove 5 hours ]

Extra's further investigated:

if y = 5

• x = 14 - y
• x = 14 - 5
• x = 9

              [ Therefore Ben drove 9 hours ]

Answer 2

Answer:

Landon drove 5 hours (and Ben drove 9 hours)

Step-by-step explanation:

Let B = number of miles Ben drove

Let L = number of miles Landon drove

Given The trip took them 14 hours

⇒ B + L = 14

Given, Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. Ben and Landon took turns driving on a 820 mile road trip:

⇒ 60B + 56L = 820

Rewrite B + L = 14 to make B the subject, substitute into 60B + 56L = 820, and solve for L:

⇒ B = 14 - L

⇒ 60(14 - L) + 56L = 820

⇒ 840 - 60L + 56L = 820

⇒ 20 = 4L

⇒ L = 5

Therefore, Landon drove for 5 hours