A rectangular tank measuring 60 cm by 40 cm and 20 cm was 1/6 filled with water. At 08 00, Tap A with water flowing out at a rate of 3 litres per minute was turned on. At 08 02, Tap B was turned on to drain water out of the container at a fixed rate. At 08 13, the tank was 75% filled with water. At what time would the tank be filled to the brim?
Solution
Capacity of tank -----
(60 cm x 40 cm x 20 cm) = 48 000 cubic cm or 48 000 ml
1/6 of volume ----- 48 000 ml x 1/6 = 8000 ml
Water flowed for 2 min ----- 3 litres x 2 = 6000 ml
Amount of water in tank at 08 02 -----
8000 ml + 6000 ml = 14000 ml
75% volume ----- 48 000 ml x 75% = 36 000 ml
From 08 02 to 08 13 ----- 11 min
Rate of increase of water level in tank -----
(36 000 – 14 000) ml divided by 11 min
= 2000 ml per min
To be filled to the brim from 75% volume, another 25% volume must be filled.
25% volume ---- 48 000 ml x 25% = 1200 ml
Time needed ----- 12 000 ml divided by 2000 ml per min = 6 min
6 min after 08 13 is 08 19
Answer: It would be 08 19 when the tank is filled to the brim.
Thursday, August 28, 2008
Pei Chun Public Sch 2007 PSLE Math Prelim Q46
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3 comments:
Sir,
PSLE Mathematics is just a few weeks from now. As such, I have an unsolved question that i have attempted ample times but still can't derive the answers. Hope that you can provide me the solution with explanation to better prepare me for the exam. I am stuck on question (b). Please help.
The questiion is below:
Melvin filled an empty rectangular tank measuring 30 cm by 20 cm by 27 cm with water using 2 taps, Tap A and Tap B. Tap A, alone, can fill the empty tank in 3 hours while Tap B, alone, can fill it up in 2 hours. Melvin turned on Tap A for 5 minutes before turning on Tap B. Both taps were then left on for half an hour before they were turned off.
(a) What fraction of the tank was filled after 5 minutes?
(b) How much more water was required to fill the tank after 35 minutes? Give your answer in litres.
The answers are
a)1/36 tank
b)2.25 litres
Extracted:
Melvin filled an empty rectangular tank measuring 30 cm by 20 cm by 27cm with water using 2 taps, Tap A and Tap B. Tap A, alone, can fill the empty tank in 3 hours while Tap B, alone, can fill it up in 2 hours. Melvin turned on Tap A for 5minutes before turning on Tap B. Both taps were then left on for half an hour before they were turned off.
(a) What fraction of the tank was filled after 5 minutes? [2]
(b) How much more water was required to fill the tank after 35 minutes? Give your answer in litres. [3]
There are many ways to solve this problems....I am sure many can solve part (a).
Below are the 2 methods:
Method 1: Fraction
(a) For Tap A:
3 hours -----> 1 whole tank
1 hour -----> 1/3 tank
1/12 hrs-----> 1/36 tank
(b) For Tap A :
3 hours -----> 1 tank
1 hour -----> 1/3 tank
1/2 hr -----> 1/6 tank
For Tap B :
2 hours -----> 1 tank
1 hour -----> 1/2 tank
1/2 hr -----> 1/4 tank
In 1/2 hrs:
Tap A + Tap B = 1/6 + 1/4
= 5/12 tank filled
In 35 mins:
1/36 + 5/12
= 16/36 filled with water
1 - 16/36 = 20/36
= 5/9 unfilled with water
Therefore,
5/9 * 30 * 20 * 27 = 9000 ml
= 9 litres
Method 2 : Whole numbers
(b)
Volume of tank = 30 * 20 * 27
= 16200 ml
Rate of water for Tap A :
180 mins -----> 16200 ml
1 min -----> 90 ml
Rate of water for Tap B :
120 mins -----> 16200 ml
1 min -----> 135 ml
In 1 min,
rate of both Tap A and Tap B
= 90 + 135
= 225 ml
For the first 5 mins,
it was filled by Tap A alone
= 5 min * 90 ml
= 450 ml
For the next 30 mins,
it was filled by both Tap A and B
= 30 mins * 225 ml
= 6750 ml
Remaining water that is required to fill the tank:
16200 ml - 450 - 6750 = 9000 ml
= 9 litres
Basically you can omit some of the steps.
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