MATH HOMEWORK, VERY URGENT. PLEASE HELP! WHAT IS...?

Question

4. Alcohol and water are mixed in the ratio 1:4 by volume. If the volume of the solution is 600 cm,
a) Find the volume of the alcohol in the solution
b) Fine the volume of the water in the solution
c) How much alcohol must be added to the solution so that the ratio of alcohol to water in the solution becomes 1:3 by volume?

5. A mental bar of mass 3.6kg is cut into two pieces in the ratio 3:5. The length of the shorter please is 45cm. Find
a) The length of the longer piece,
b) The length of the original metal bar
c) Its rate of mass per unit length in kg/m
d) The mass of the shorter piece

6. a) Simplify each of the following ratios.
i) a:b = 1 1/2 : 2 2/5 ii) b:c = 0.105:0.350
b) Find the ratio a:b:c using the data in (a)
c) Alan, Bob and Cathy share $500 in the ratio a:b:c found in (b). Find Alan's share correct to 2 decimal places.

7. A 2 liter bottle of peanut oil is sold for $15. A 2 1/2 liter bottle of olive oil is sold for $30.
a) Find the unit price x of peanut oil in $/l
b) Find the unit price y of olive oil in $/l
c) Find the ratio x:y
d) Suppose both types of oil are equally good for cooking, which one is a better buy?
e) The bottle of peanut oil can be used for 16 days. Find its consumption rate in /l day
f) If the consumption rate of the bottle of olive oil is the same as that of peanut oil, how long can it last?

8. A man took 4 1/2 hours to drive 360km from Singapore to Kuala Lumper. He used 37.5 liters of petrol for the entire journey.
a) Find his average speed
b) Find the petrol consumption rate in km/l
c) He drove an average speed of 110km/h on a highway for 2 hours during his journey. Find his average speed for the remaining part of his journey.

9. A car starts from rest. After traveling 125m in 10s, its speed picks up to 25m/s. It travels at this speed for 20 seconds. Then the brakes are applied. The car stops in 6 seonds and the braking distance is 95m.
a) Express the speed 25 m/s in km/h.
b) Find the average speed of the car during the period at which its speed increases.
c) Find the average speed of the car during the period the brakes were applied.
d) Find the average speed of the car for the whole journey.

10. Towns P and Q are 120km apart. Mr. Tan drove from P to Q and was scheduled to reach Q after 2 hours. His average speed was 54 km/h for the first 40 minutes.
a) What was his average speed for the remaining journey if he managed to arrive just on time?
b) The time taken for his return journey is 2 hours and 10 minutes. Find his average speed for
(i) The return journey (ii) The whole trip.

Answer 1

Alcohol and water are mixed in the ratio 1:4

So, The volume of the alcohol in the solutions is x (say)

And the volume of the water in the solutions is 4x (say)

Given that the volume of the solutions is 600 cm,

i.e. x+4x = 600

5x = 600

Divide each side by 5.

x = 120 cm

a) The volume of the alcohol in the solutions is x = 120 cm

b) The volume of the water in the solutions is 4x = 4(120) = 480 cm

c) the ratio of alcohol to water in the solution becomes 1:3 by volume.

i.e. x+3x = 600

4x = 600

Divide each side by 4.

x = 150

The alcohol must be added to the solution is x = 150.

Answer 2

A mental bar of mass 3.6 kg is cut into two pieces in the ratio 3 : 5.

Let The length of the longer piece is 5x

Let The length of the shorter piece is 3x.

i.e. 3x = 45 ⇒ x = 15

a) The length of the longer piece is 5x = 5(15) = 75 cm

b) The length of the original metal bar is (shorter+longer) piece= 45+75 = 120 cm

c) Its rate of mass per unit length is 3.6kg/120cm = 3.6kg/1.2m = 3:1           [1 cm = 0.01m]

d) The mass of the shorter piece is (45)(3) = 135 kg.

Answer 3

6). a). i). a : b = 1 1/2 : 2 2/5

Rewrite the mixed numbers as improper fractions.

a : b = 3/2 : 12/5

The LCM of 2, 5 is 10

Multiply each number by 10.

a : b = 30/2 : 120/5 = 15 : 24

Divide each number by 3.

a : b = 5 : 8.

ii). b:c = 0.105:0.350

Multiply each number by 1000.

b : c = 105 : 350 = 3 : 10

b) the ratio a:b = 5 : 8

Multiply each number by 3.

So, a : b = 15 : 24

and b : c = 3 : 10

Multiply each number by 8.

b : c = 24 : 80

a : b : c = 15 : 24 : 80

c) Alan, Bob and Cathy share $500 in the ratio a:b:c

Le t Alan's share is 15x, Bob's share is 24x and Cathy's share is 80x.

15x+24x+80x = 500

119x = 500

Divide each side by 119.

x = 4.201

Alan's share is 15(4.201) = 63.015.