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Two drivers, Jada and Zach, enter Highway 98 at the same time, both going west. Jada's entrance is 43.4 miles west of Rockport City, and Zach's entrance is 56.2 miles west of Rockport City. Jada drives 70 miles per hour, and Zach drives 62 miles per hour.

If they each keep a constant speed, how many hours will it take for Jada to pass Zach on the highway?
Simplify any fractions.

1 answer

To determine how long it will take for Jada to pass Zach, we first need to establish their starting positions and speeds.

  1. Starting Positions:

    • Jada starts 43.4 miles west of Rockport City.
    • Zach starts 56.2 miles west of Rockport City.

  2. Relative Positioning: To find out how far behind Zach is from Jada when they start: \[ \text{Distance between Jada and Zach} = 56.2 \text{ miles} - 43.4 \text{ miles} = 12.8 \text{ miles} \] This means Zach is 12.8 miles behind Jada at the start.

  3. Speeds:

    • Jada's speed = 70 miles per hour.
    • Zach's speed = 62 miles per hour.

  4. Relative Speed: To find the rate at which Jada is gaining on Zach, we calculate the difference in their speeds: \[ \text{Relative speed} = \text{Jada's speed} - \text{Zach's speed} = 70 \text{ mph} - 62 \text{ mph} = 8 \text{ mph} \]

  5. Time to pass: To determine how long it will take for Jada to cover the 12.8 miles distance between them at their relative speed: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{12.8 \text{ miles}}{8 \text{ mph}} = 1.6 \text{ hours} \]

Thus, it will take Jada 1.6 hours to pass Zach on the highway.