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.

Answer 1

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 * Time`

Distance (Jessica) =
`21 * (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 * Time`

Distance (Alberto) =
`35 * 3\\` = 105 miles ...................Equation (2)

Equating both the distances in equation 1 & 2

`21 * (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.