a = 4800 – 6t
b = 5400 – 8t

In the system of equations above, a and b represent the distance, in meters, two marathon runners are from the finish line after running for four hours and t seconds. How far will runner a be from the finish line when runner b passes her?

A. 300 meters
B. 500 meters
C. 100 meters
D. 3000 meters

 

Runner b will pass runner a when they are the same distance from the finish line, so set those distance expressions equal.

4800-6t=5400-8t
2t=600
t=300

But be careful, t is not a measure of distance, it’s time! The runners will meet at 300 seconds from the 4 hour mark. To find the distance they’ll be from the finish line at that time, plug 300 back into one of the original equations.

a=4800-6(300)
a=3000

So the answer is D.