Problem 17 · 2014 Math Kangaroo
Medium
Ratios, Rates & Proportions
distance-speed-time
Anna walks a distance of 8 km at a speed of 4 km/h. Then she runs for a while at 8 km/h. For how many minutes must she run so that her overall average speed is 5 km/h?
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Answer: E — 40 min
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Hint 1 of 2
Average speed is total distance over total time, not the average of the speeds.
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Hint 2 of 2
Write the running distance as an unknown and set the overall average to 5 km/h.
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Approach: set total distance / total time = 5
- Walking 8 km at 4 km/h takes 2 h. Let the run be d km at 8 km/h, taking d/8 h.
- Require (8 + d)/(2 + d/8) = 5; solving gives d = 16/3 km.
- Running time = (16/3)/8 h = 2/3 h = 40 min.
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