F.2Maths唔識做~Ratio and Rate

10) .a)
For 50% alcohol, the volume of alcohol and volume of water should be equal. Since Kelvin has 6L of alcohol and 4 L of water, Kelvin only has to add 2L of water to his mixture, so that finally he has 6L of alcohol and 6L of water.
Volume of solution 6L + 6L = 12 L
Volume of alcohol = 6L
Percentage of alcohol in solution
= (Volume of alcohol/volume of solution)x 100% = (6L/ 12L) x 100% = 50%

Kelvin should add 2L of water to the mixture. (answer)

b)
If they mix their mixture together,
Volume of alcohol = 6L + 3L = 9L
Volume of water =4L + 5L = 9L
Let y be the volume of alcohol added to make 75% alcohol
9L + y
-------- X 100% = 75%
18 + y
100(9 + y) = 75(18 + y)
900 + 100y = 1350 + 75y
100y – 75y = 1350 – 900
25y = 450
y = 450/25 = 18

18 L alcohol should be added to their mixture so that there is 75% alcohol. (answer)

11)
a)
time required = distance/speed
Time required for car A to travel 100m = 100 m/2m/s = 50 s
Time required for car B to travel 100m = 100 m/3m/s = 33 1/3 s

Difference in time = 50 s – 33 1/3 s = 16 2/3 s or 16.66 s (answer)

b)
Alvin increases car A’s speed to 4 m/s
Time required for car A to travel 100m if the new speed is 4 m/s = 100 m/4m/s = 25 s
For car B to finish the track ahead of car by 5 seconds, time required by car B to finish the track = 25 s – 5s = 20 s
The new speed of car B = distance/time = 100 m/20 c = 5 m/s

Perentacge increase in the speed of car B
= (increase in speed/original speed) X 100% =[ (5 m/s – 3 m/s)/ 3 m/s] X 100%
= [2m/s/3 m/s] x!100% = 66 2/3 % or 66.67% (Answer)