A question from Applerouth’s Guide to the New SAT in the chapter “Solving Systems” of equations (p. 503):

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) 200 meters
B) 300 meters
C) 1000 meters
D) 3000 meters

Answer is supposed to be D.
(No idea how to solve!)

I guess you’re supposed to assume that, despite the fact that a is currently closer to the finish line and they’ve been running for the same amount of time, b is currently running faster than a. I guess you’re also meant to assume that a is now running at a constant rate of 6 meters per second and b is now running at a constant rate of 8 meters per second, and that both runners will continue at those paces until b passes a. That’s a lot of assumptions that you wouldn’t have to make on a real SAT question.

b will pass a when ba, so you can set the equations equal to solve for t:

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

That tells you that b will catch up to a in 300 seconds. To figure out how far they’ll be from the finish line at that point, plug 300 into either equation:

a = 4800 – 6(300)
a = 4800 – 1800
a = 3000

Leave a Reply