O lvl E Maths: Ratio Rate Proportion

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A rectangular pool can be filled by two pipes together in 6 hours. The smaller pipe alone takes 5 hours longer than the larger pipe to fill the pool. Find them time each pipe will take to fill the pool on its own.

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Answer:

Let the time taken by small pipe alone = Ts
Let the time taken by bigger pipe alone = Tb
Let Volume of pool = V

So

Rate of flow of small pipe = V/Ts
Rate of flow of bigger pipe = V/Tb

Get the equations out

Ts - Tb = 5
Ts = Tb + 5 ------------- (1)

V / ( V/Ts + V/Tb) = 6
TsTb / (Ts + Tb) = 6
Ts Tb = 6Ts + 6 Tb
Sub (1) into equation
Tb² + 5Tb = 6Tb + 30 + 6 Tb
Tb² - 7Tb - 30 = 0

Solving, Tb = 10 hours or -3 (reject)
Hence, Ts = 15 hours

O lvl E Maths: Ratio Rate Proportion

RI 1998 Sec 3 EOY Q2

3 men, working 8 hours a day, can finish a job in 6 days. How many days would it take 2 men working 9 hours a day to complete the same job, assuming that they work at the same rate?

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Answer:

Total number of man-hours when 3 men are working 8 hours a day for 6 days
= (3 * 8 * 6) man-hours

Days taken to complete when 2 men are working 9 hours a day
= (3 * 8 * 6) / (2 * 9)
= 8 days

O lvl E Maths: Ratio Rate Proportion

Dunman High Prelims 2008 P1 Q8

A swimming pool can be filled by a large pipe operating alone in 3 hours. If the pool is filled by the small pipe alone, it will take t hours longer than the larger pipe filling it alone. And it will take 2 hours for both pipes to fill up the pool. Find the value of t.

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Answer:

Operating alone, the large pipe fills 1/3 of the swimming pool in 1 hour.

Operating alone, the small pipe fills 1/(3+t) of the swimming pool in 1 hour.

Operating together, two pipes fill 1/3 + 1/(3+t) of the swimming pool in 1 hour.
Since it takes 2 hours for both pipes to fill up the pool, both pipes will fill 1/2 of the pool in 1 hour.

Hence, 1/3 + 1/(3+t) = 1/2
1/(3+t) = 1/2 - 1/3
1/(3+t) = 1/6
3+t = 6
hence, t = 3

O lvl E Maths: Ratio Rate Proportion

(1) A construction project consisting of 12 semi-detached houses can be completed in 18 months by 54 men. Find the number of men required to complete another similar project consisting of 35 semi detached houses which must be built in 12 months.


(2) The size if Singapore on a map with a scale of 1:50000 is reflected as 2730.8 cm² and the coastline is reflected as 386cm. The size of Singapore when drawn on another map of a different scale is 10923.2 cm². Find the length of coastline as reflected on this second map.

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Answer:

(1)

12 houses-----18 months------- 54men
1 house------1.5 month-------- 54men (use 18 divide by 12 to get 1.5)
36 houses------54 months------- 54 men (1.5 x 36 will get 54, this is working with 54men)

So if I want to complete the house in 12 months,

36 house----54 months----- 54men
36 house----1 month---- 54*54 = 2916 men
36 house----12 months---- 2916/12 = 243 men

Thus, 243 men are required to complete another similar project consisting of 35 semi detached houses which must be built in 12 months.

(2)

The difference in ratio between the two maps is

sqrt( 10923.2 / 2730.8 ) = 2

so, coastline of second map / 386 = 2 (not area, so dun need to square it)

coastline of second map = 2 * 386 = 772