Question

Alex and Jenna set off traveling due north from their separate houses to go on a long distance bike ride. Alex lives 20 miles north of Jenna, and travels at 11 miles per hour. Jenna travels at 13 miles per hour. Using the system of equations shown, determine how many hours, x, and miles, y, Alex and Jenna traveled when Jenna caught up with Alex.

11x-y=-20
y=13x
Complete the statement. Jenna and Alex had traveled___ hours and____ miles when Jenna caught up with Alex.

Answer 1

Jenna and Alex had traveled 10 hours and 130 miles when Jenna caught up with Alex. This is determined by solving the system of linear equations given for the two cyclists.

Step-by-step explanation:

To solve the problem of determining how many hours, x, and miles, y, Alex and Jenna traveled when Jenna caught up with Alex, we'll need to solve the system of equations provided:

⇒11x - y = -20 (1)

⇒y = 13x (2)

Substitute equation (2) into equation (1) to find x:

1. 11x - (13x) = -20
2. -2x = -20
3. x = 10

Now we know that Jenna and Alex have been traveling for 10 hours. To find y, the distance, we substitute x back into equation (2):

1. y = 13 * 10
2. y = 130 miles

Jenna and Alex had traveled 10 hours and 130 miles when Jenna caught up with Alex.

The solution involves solving a system of equations for hours (x) and miles (y) traveled by Alex and Jenna. By substituting equation (2) into equation (1) and solving, x is found to be 10 hours. Substituting x back into equation (2) gives y as 130 miles.

Thus, Jenna caught up with Alex after 10 hours, covering a distance of 130 miles.