Two skaters are racing toward a finish line of a race. The first skater has a 40 meter lead and is traveling at a rate of 12 meters per second. The second skater is traveling at a rate of 14 meters per second. How long will it take for the second skater to pass the first skater?

20 seconds

Step-by-step explanation:

speed = distance/time

distance = speed * time

The faster racer will catch up to the slower racer in x meters ahead of the slower racer.

The faster racer is 40 meters behind the slower racer, so he travels x + 40 until he catches up.

Slower racer:

speed = 12 m/s

distance = x

time = t

Faster racer:

speed = 14 m/s

distance = x + 40

time = t (the same time as the slower racer)

Slower racer:

distance = speed * time

x = 12t

Faster racer:

x + 40 = 14t

System of equations:

x = 12t

x + 40 = 14t

Since the fist equation is already solved for x, substitute 12t for x in the second equation and solve for t.

12t + 40 = 14t

40 = 2t

20 = t

t = 20

The faster racer catches up in 20 seconds.