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.
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.
So the answer is D.
Thanks, Mike! Much appreciated!