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Math Kangaroo practice

Name: ______________________Date: ____________2 questions · 7 points

1.Two towns are 300 km apart. A car leaves each town at the same moment driving toward the other, one at 60 km/h and the other at 90 km/h. How long until they meet?[3]
- A2 hours
- B3 hours 20 minutes
- C4 hours
- D5 hours
- E1 hour
2.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
- A40 percent
- B37.5 percent
- C75 percent
- D35 percent
- E30 percent

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Answer key — Math Kangaroo practice

Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.

1.A — 2 hoursKA-0162Rate, time, distance
- BI used only the slower car's speed and divided 300 by 90 the wrong way round.
- CI averaged the two speeds to 75 km/h and divided 300 by it, which ignores that both cars move at once.
- DI divided 300 by 60, using only the slower car.
- EI halved the distance to 150 and then divided by 150, applying the closing speed twice.
2.A — 40 percentKA-0165Mixtures and weighted averages
- BI averaged 25 and 50 without weighting by how much of each solution there was.
- CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
- DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
- EI used only the acid from the weaker solution and spread it over all ten litres.

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