Question

Herbert and Samantha are both driving from Orlando to Miami. Herbert leaves at 9:00 and averages 60 mph (miles per hour) on the way. Samantha leaves at 9:10 and averages 65 mph on the way. The situation is modeled by this system, where x is the number of hours after Samantha leaves and yis the distance each will travel: y = 60x + 10 y = 65x How long after Samantha leaves will she pass Herbert, and how far will they each have traveled?​

Answer 1

Option B

Explanation:

We first set the two equations equal to each other.

y = 60x + 10

y = 65x

Equal Values Method:

y = y, so:

60x + 10 = 65x

Solve:

• 60x + 10 = 65x
• 10 = 5x
• x = 2

We can input 2 into either of the original equations

• y = 60x + 10
• y = 60(2) + 10
• y = 120 + 10
• y = 130

The correct option is
`\boxed{\text{B}}`

-Chetan K

Answer 2

• Option B

Explanation:

At the point they meet, they both travel same distance.

Make the equations same and solve for x:

• 60x + 10 = 65x
• 65x - 60x = 10
• 5x = 10
• x = 2

They will meet after 2 hours.

The distance traveled at the time is:

• 65*2 = 130 miles

Correct choice is B