1.
A rope footbridge holds at most 50 kg at one time. Hamza weighs 25 kg, Bilal 20 kg, and Layla 30 kg. Which pairs are allowed to cross together? Can all three cross at once?
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Answer:
Did you know? In Peru, villagers rebuild the Q'eswachaka rope bridge by hand every year, weaving the whole thing out of grass.
2.
The stone arches under an old bridge are numbered in order: 3, 6, 9, 12, ___, ___ . What are the next two numbers, and what is the rule?
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Answer:
Did you know? The AlcΓ‘ntara Bridge in Spain was built by Roman engineers around the year 106, and it still stands today.
3.
One morning 15 boats passed under the bridge. There were 5 more sailboats than motorboats. How many of each? (Hint: try pairs that add to 15.)
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Answer:
Did you know? Some bridges split in the middle and tilt upward to let tall ships through. London's Tower Bridge still opens about 800 times a year.
4.
Four bridges cross the same river: Iron, Stone, Rope, and Wood. Stone is the furthest north. Wood is the furthest south. Rope is just north of Wood. List all four in order from north to south.
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Answer:
Did you know? The city of Venice is built on water and has around 400 bridges β many so small only people on foot can use them.
5.
Musa is building a model bridge. The deck can be wood or steel, and the cables can be red, blue, or green. How many different models can he build? List them all.
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Answer:
Did you know? Each main cable on the Golden Gate Bridge is a bundle of 27,572 thin steel wires β thinner than a pencil, all pressed together.
1.
A bridge toll: a car costs 4 dirhams, a truck 9, and any crossing after sunset costs 5 extra. Yusuf's family made 3 car and 2 truck crossings, 1 of them after sunset. Amina's made 5 car and 1 truck crossing, 2 after sunset. Who paid more, and by how much?
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Answer:
Did you know? Old London Bridge had shops and houses built on top of it, some seven storeys tall.
2.
Yusuf, Khadija, and Tariq each inspected a different bridge (Iron, Rope, Stone) on a different day (Mon, Wed, Fri). Who did which, and when?
1. Khadija did not inspect the Rope bridge. 2. Tariq inspected on Friday. 3. The Iron bridge was inspected on Monday, and not by Khadija.
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Answer:
Did you know? US law requires most bridges to be inspected at least once every two years.
3.
A rope bridge is laid with 64 original planks. Every year a storm takes out half of the original planks still remaining, and new ones replace them. After 5 years, how many original planks are left? How many were replaced in all?
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Answer:
Did you know? A rope bridge sways on purpose. A bridge that cannot move at all cracks when the wind pushes on it.
4.
Two bridges carried 132 vehicles between them in one hour. The Iron bridge carried 24 more than the Stone bridge. How many did each carry?
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Answer:
Did you know? The Akashi KaikyΕ Bridge in Japan hangs across a gap of 1,991 metres β almost two kilometres between its towers.
5.
Four people cross a dark rope bridge with one lantern. It holds 2 at a time, the lantern must go with them, a pair moves at the slower one's speed, and someone must carry the lantern back. Yusuf takes 1 minute, Musa 2, Baba 5, Dadi 10. What is the fastest they can all be across?
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Answer:
Did you know? Before electric light, bridge keepers walked out each evening to light oil lamps along the whole span by hand.
3rd Grade
1. Hamza+Bilal (45) and Bilal+Layla (50) may cross. Hamza+Layla (55) may not. All three = 75 kg, too heavy.
25+20 = 45 β Β· 20+30 = 50, exactly the limit, so allowed ("at most 50") Β· 25+30 = 55 β Β· 75 β.
2. 15 and 18. Rule: add 3 each time (the multiples of 3).
12 + 3 = 15, 15 + 3 = 18.
3. 10 sailboats, 5 motorboats.
Take the 5 off first: 15 β 5 = 10, then 10 Γ· 2 = 5 motorboats. Sailboats = 10. Check: 10+5 = 15 β, 10β5 = 5 β.
4. Stone, Iron, Rope, Wood.
Stone 1st, Wood 4th. Rope is just north of Wood β 3rd. Only Iron is left β 2nd.
5. 6 models.
2 decks Γ 3 colours = 6: wood-red, wood-blue, wood-green, steel-red, steel-blue, steel-green.
4th Grade
1. Amina paid more β 39 to Yusuf's 35, so by 4 dirhams.
Yusuf: (3Γ4)+(2Γ9)+(1Γ5) = 12+18+5 = 35. Amina: (5Γ4)+(1Γ9)+(2Γ5) = 20+9+10 = 39. 39β35 = 4.
2. Yusuf β Iron β Monday Β· Khadija β Stone β Wednesday Β· Tariq β Rope β Friday.
Clue 3: Iron is Monday, not Khadija. Clue 2 puts Tariq on Friday, so not Monday β Yusuf, Iron, Monday. Clue 1: Khadija isn't Rope and Iron is taken β Khadija, Stone. Tariq takes Rope on Friday, so Khadija is Wednesday.
3. 2 original planks left; 62 replaced.
64 β 32 β 16 β 8 β 4 β 2 (5 halvings). Replaced: 64 β 2 = 62.
4. Iron 78, Stone 54.
Take the 24 off first: 132 β 24 = 108, then 108 Γ· 2 = 54 Stone. Iron = 78. Check: 78+54 = 132 β, 78β54 = 24 β.
5. 17 minutes.
Yusuf+Musa cross (2) Β· Yusuf back (1) Β· Baba+Dadi cross together (10) Β· Musa back (2) Β· Yusuf+Musa cross (2) = 17. The trick: send the two slowest together so the 5 hides inside the 10.