Respuesta :
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:
[tex]Distance = Speed \times Time[/tex]
Distance (Jessica) = [tex]21 \times (t+3)[/tex] ...................Equation (1)
Alberto traveled for 3 hours at an average speed of 35 miles per hour (mph) so, total distance covered by Alberto is:
[tex]Distance = Speed \times Time[/tex]
Distance (Alberto) = [tex]35 \times 3\\[/tex] = 105 miles ...................Equation (2)
Equating both the distances in equation 1 & 2
[tex]21 \times (t+3) = 105[/tex]
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.
