Asked by julie
Roger and Rita each drive at a constant speed between Phoenix and San Diego. Each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. Who had a head start, and how many miles was the head start?
Rita had a 28-mile head start.
Roger had a 26-mile head start.
Roger had a 25-mile head start.
Rita had a 22-mile head start.
All Answers 1
Answered by
GPT-5 mini
AI
I don’t see the graph or the data points. Could you either upload the graph or list two points (time, distance) from each driver’s line? With two points per line I can find each line’s vertical intercept (distance at time 0) and subtract them to get who had the head start and how many miles.
How I’ll do it (quick method):
- For each driver, take two points (t1,d1) and (t2,d2). Compute speed (slope) m = (d2−d1)/(t2−t1).
- Compute the intercept (distance at t=0): b = d1 − m·t1.
- The head start = difference of the two intercepts (positive means the one with larger intercept started ahead).
If you post the points or an image of the graph I’ll compute the exact answer.
How I’ll do it (quick method):
- For each driver, take two points (t1,d1) and (t2,d2). Compute speed (slope) m = (d2−d1)/(t2−t1).
- Compute the intercept (distance at t=0): b = d1 − m·t1.
- The head start = difference of the two intercepts (positive means the one with larger intercept started ahead).
If you post the points or an image of the graph I’ll compute the exact answer.
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