Problem 18 · 1992 AJHSME
Medium
Ratios, Rates & Proportions
average-speed
On a trip, a car traveled 80 miles in an hour and a half, then was stopped in traffic for 30 minutes, then traveled 100 miles during the next 2 hours. What was the car's average speed in miles per hour for the 4-hour trip?
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Answer: A — 45.
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Hint 1 of 3
Average speed is NOT the average of the speeds. It's about the whole journey: how far in total, over how long in total — and does the clock keep ticking while the car sits in traffic?
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Hint 2 of 3
Average speed = total distance ÷ total time. The total time must include every minute the trip took, even the stopped half-hour.
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Hint 3 of 3
Add the two driving distances; add all three time chunks (including the stop) for the bottom.
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Approach: total distance ÷ total elapsed time (stop included)
- Total distance driven: 80 + 100 = 180 miles. Total time elapsed: 1.5 hr driving + 0.5 hr stopped + 2 hr driving = 4 hours — the stop still counts.
- Average speed = 180 ÷ 4 = 45 mph.
- Why this transfers: average speed always means ‘if you'd gone one steady speed the whole time, what would it be?’ — so it's total distance over total time, never the plain average of the leg-speeds.
- Trap: the leg speeds are about 53 mph and 50 mph; averaging those to ~52 ignores the half-hour of zero. Including the stop drags the true average down to 45.
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