Problem 15 · 2024 Math Kangaroo
Hard
Logic & Word Problems
substitutionsum-constraint
The two pictures show the same bridge at different times. All the cars are the same length. The numbers give the distances between the cars, and between a car and the end of the bridge. How long is each car?
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Answer: C — 5 metres
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Hint 1 of 3
It is the same bridge in both pictures, so the bridge is exactly the same total length both times.
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Hint 2 of 3
In each picture add up all the gap numbers, and count how many cars there are.
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Hint 3 of 3
The bottom picture has one fewer car but more gap — that extra gap must be exactly one car long.
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Approach: the same bridge length both times
- Top picture: the gaps add to 1 + 2 + 1 + 2 = 6 metres, and there are 3 cars.
- Bottom picture: the gaps add to 4 + 4 + 3 = 11 metres, and there are 2 cars; the bridge is the same length, so the bottom has 11 − 6 = 5 more metres of gap but exactly one fewer car.
- That missing car is filling those extra 5 metres of gap, so each car is 5 metres long.
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