Problem 11 · 2020 AMC 8
Easy
Ratios, Rates & Proportions
distance-speed-timegraph-reading
Show answer
Answer: E — 24 mph.
Show hints
Hint 1 of 2
Average speed ignores every stop, wiggle, and flat spot in the graph — it only looks at the two endpoints. So all you need is each girl's finishing time at 6 miles.
Still stuck? Show hint 2 →
Hint 2 of 2
Read where each line hits 6 miles: Naomi at 10 min, Maya at 30 min. Convert each to miles per hour, then subtract.
Show solution
Approach: average speed depends only on start and finish
- Average speed = total distance ÷ total time, so the bumps in the graph don't matter — only the endpoint times do. Read them off: Naomi hits 6 miles at 10 min, Maya at 30 min.
- Naomi: 6 miles in 10 min = 16 hr → 6 ÷ 16 = 36 mph.
- Maya: 6 miles in 30 min = 12 hr → 6 ÷ 12 = 12 mph.
- Difference: 36 − 12 = 24 mph.
- Why this transfers: on a distance–time graph, average speed is just the slope of the straight line from start to finish — the actual path's twists are irrelevant. Don't get baited into measuring individual segments.
Another way — same distance → compare the times:
- Both travel the same 6 miles, so their speeds are in reverse ratio to their times: Naomi (10 min) is 3 times faster than Maya (30 min).
- Maya is 12 mph, so Naomi is 36 mph, and the gap is 36 − 12 = 24 mph — no need to recompute from scratch.
Mark:
· log in to save