Problem 26 · 2025 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
Julia and her little sister Paula start a bike ride together. Julia cycles at a constant speed of 18 km/h and Paula at a constant speed of 12 km/h. They cycle along the same route. After 20 minutes, Julia is tired and turns around. When she meets Paula, she also turns around and they both cycle home at their respective speeds. How many minutes does Paula arrive later than Julia?
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Answer: C — 8
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Hint 1 of 2
Find where Julia (turning at 20 min) meets Paula, then send each home at her own speed.
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Hint 2 of 2
They meet 4 min after Julia turns; from there compare each rider's time home.
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Approach: meeting point then separate trips home
- In 20 min Julia rides 6 km and turns; Paula has ridden 4 km. Closing 2 km at 30 km/h takes 4 min, meeting at 4.8 km.
- Julia home: 24 + 4.8/18·60 = 40 min. Paula home: 24 + 4.8/12·60 = 48 min.
- Paula arrives 8 minutes later.
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