Anonymous
Anonymous asked in 科學及數學數學 · 6 years ago

F.4 math questions

1. Pipe A takes 12 hours to fill up a tank.

Pipe B takes 8 hours to fill up the tank.

Pipe A and pipe B are turned on at the same time , how long will they take to fill up the tank?

2.If a=2b=3c , 1/a: 1/b : 1/c = ??

3. the scale of map is 1 : 2000. If the area of a park is 12cm² on the map , its actual area is ? ?

Just answer as many as you can. thx

1 Answer

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  • 6 years ago
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    1.

    Pipe A takes 12 hours to fill up a tank.

    ⇒ In 1 hour, pipe A can fill up 1/12 of a tank.

    Pipe B takes 8 hours to fill up the tank.

    ⇒ In 1 hour, pipe B can fill up 1/8 of a tank.

    Therefore, in 1 hour, pipe A and pipe B together can fill up

    1/12 + 1/8

    = 2/24 + 3/24

    = 5/24 of a tank.

    The time it takes for both pipes together to fill up the tank is

    1/(5/24) = 24/5 = 4.8 hours.

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    2.

    Let a = 2b = 3c = 6k where k is a non-zero constant.

    Then, b = 3k and c = 2k.

    1/a : 1/b : 1/c

    = 1/(6k) : 1/(3k) : 1/(2k)

    = 1/6 : 1/3 : 1/2

    = 6/6 : 6/3 : 6/2

    = 1 : 2 : 3

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    3.

    The scale of map is 1 : 2000.

    That means, 1 cm on the map refers to 2000 cm in actual place.

    1 cm² = (1 cm) × (1 cm) on the map

    refers to (2000 cm) × (2000 cm)

    = (20 m) × (20 m)

    = 400 m² (or 4000000 cm²) in actual place

    Therefore, 12 cm² on the map refers to

    12 × 400 m² = 4800 m² in the actual place.

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