Question

PLEASE HELP!!!

Ralph and Liza are both driving fro Los Angeles to Santa Fe. Ralph leaves at 7:00 and averages 60 mph (miles per hour) on the way. Liza leaves at 7:25 and averages 65 mph on the way. The situation is modeled by this system, where x is number of hours after Liza leaves and y is the distance each will travel:

y=60x+25
y=65x

How long after Liza leaves will she pass Ralph, and how far will they each have traveled?

A. Liza will not pass Ralph, because she will never catch up with him.

B. Liza will pass Ralph after 3 hours, and they each will have traveled 205 miles.

C. Liza will pass Ralph after 5 hours, and they each will have traveled 325 miles.

D. Liza will pass Ralph after 4 hours, and they each will have traveled 260 miles.

Answer 1

To find the time and distance at which Liza passes Ralph, we need to solve the system of equations.

Subtracting the first equation from the second, we get:

65x - 60x = y - 25

5x = y - 25

y = 5x + 25

Substituting this value of y into the first equation, we get:

60x + 25 = 5x + 25

55x = 0

x = 0

This means that Liza will pass Ralph 0 hours after she leaves, or at the same time as Ralph. At this time, they will have both traveled 0 miles.

Therefore, the answer is A: Liza will not pass Ralph, because she will never catch up with him.