Jessica left the hospital and traveled toward the dump at an average speed of 21 mph. Alberto left sometime later traveling in the same dire

Question

Jessica left the hospital and traveled toward the dump at an average speed of 21 mph. Alberto left sometime later traveling in the same direction at an average speed of 35 mph. After traveling for three hours Alberto caught up with Jessica. Find the number of hours Jessica traveled before Alberto caught up.

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Mộc Miên 4 years 2021-08-27T18:56:53+00:00 1 Answers 14 views 0

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  1. vankhanh
    0
    2021-08-27T18:58:37+00:00
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    Answer: Jessica traveled 5 hours before Alberto caught up.

    Explanation: Let us consider that Alberto started travelling “t” hours after Jessica, So according to the question Alberto caught up with Jessica means Distance traveled by Jessica in t+3 hours = Distance traveled by Alberto in 3 hours.  

    Jessica traveled for t+3 hours at an average speed of 21 miles per hour (mph) so, total distance covered by Jessica is:

    Distance = Speed \times Time

    Distance (Jessica) = 21 \times (t+3) ……………….Equation (1)

    Alberto traveled for 3 hours at an average speed of 35 miles per hour (mph) so, total distance covered by Alberto is:

    Distance = Speed \times Time

    Distance (Alberto) = 35 \times 3\\ = 105 miles ……………….Equation (2)

    Equating both the distances in equation 1 & 2

    21 \times (t+3) = 105

    21 t + 63 = 105

    Subtracting 63 from equation, both the sides

    21 t = 105 – 63

    21 t = 42

    Dividing the equation by 21, both the sides

    t = 2 hours.

    Jessica traveled 2 hours extra relative to Alberto.

    So Jessica traveled 5 hours (2 + 3) total, before Alberto caught up.

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