Problem 13 · 1985 AJHSME
Hard
Ratios, Rates & Proportions
distance-speed-time
If you walk for 45 minutes at a rate of 4 mph and then run for 30 minutes at a rate of 10 mph, how many miles will you have gone at the end of one hour and 15 minutes?
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Answer: B — 8 miles.
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Hint 1 of 2
The speeds are in miles per HOUR, but the times are in minutes — those units must match before you multiply. Turn 45 minutes and 30 minutes into fractions of an hour first.
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Hint 2 of 2
Distance = rate × time, done separately for the walk and the run, then added. The total time (1 hour 15 min) is a distractor — you never use it directly; it's just the two legs combined.
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Approach: rate × time on each leg
- Match the units: 45 min = 45⁄60 = 3⁄4 hour, and 30 min = 30⁄60 = 1⁄2 hour.
- Walk leg: 4 mph × 3⁄4 hr = 3 miles. Run leg: 10 mph × 1⁄2 hr = 5 miles.
- Total distance = 3 + 5 = 8 miles.
- Spot the trap: the choice '480 miles' comes from multiplying speed by minutes (10 × 30 + …) without converting to hours. Always make the time unit match the speed's unit before multiplying.
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