Advanced MathMediumTime for two cars on perpendicular roads to be a given distance apart
Advanced Math practice question
Two cars leave the same point at the same time, one travelling north at 30 kilometres per hour and the other east at 40 kilometres per hour. After how many hours will the cars be 100 kilometres apart?
Answer: 2
After t hours they are 30t and 40t from the start, at right angles: distance = √((30t)² + (40t)²) = 50t. Set 50t = 100: t = 2.
Common wrong answers
- If you answered 4
- 4 doubles the correct time.
- If you answered 10
- 10 comes from 100 ÷ (40 − 30).
- If you answered 1.43
- 1.43 comes from 100 ÷ 70, adding the speeds as if the cars moved in opposite directions.
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