F.4 math questions

Question

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

Answer 1

Favorite Answer

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.