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 By: achieve_goal (offline)  Tuesday, June 25 2013 @ 03:59 AM CDT (Read 978 times)
achieve_goal

Q1.Abdul,Bernard and Chi Hao were all standing in a straight line waiting for the race to start.
Chi Hao was 300 m ahead of Bernard and Bernard was 100m ahead of Abdul. At 9 a.m. they started the race. Abdul overtook Bernard in 5 mins. In another 5 mins,Abdul overtook Chi Hao. If Bernard's speed is 150m/min, at what time did Bernard overtake Chi Hao?

++++Abdul+++Bernard++++++++++++++++++++++++++++++++++Chi Hao++
____/_________/_______________________________________________/_
<-------------><------------------------------------------------------------------->
++++++100m++++++++++++++++++++++300m++++++++++++++++++++

Q2. A rectangular tank measuring 40 cm by 30 cm by 40 cm was 1/6 filled with water. At 0930 h, Tap X with water flowing out at a rate of 3l per minute was turned on. At 0932h, Tap Y was turned on to drained water out of the tank at a fixed rate. At 0943 h, the tank was 75% filled with water. At what time would the tank be filled to the brim?

Note : '+' to buffer up space

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Tuesday, June 25 2013 @ 09:44 PM CDT
echeewh

Hey there,

Following are my worked solutions:

Q1.
//
posted on 27 Jun
//

*** - for alignment purpose

t=0900
|------------------------------------------------------------------------------------|
|-> ** |-> *********** |->
A *** B ************ C
<100><---- 300 ---->
*** s(B )=150
********** |-> ************* |->
********** B1 ************ C1
********** |->
********** A1
********* t1=0905
************************************ |->
************************************ C2
************************************ |->
************************************ A2
*********************************** t2=0910

At t = 0900:
d(AB ) = 100m; d(BC) = 300m

time taken for A to catch up B = 5 mins
time taken for A to catch up B = [100 ÷ {s(A) - 150}] , where s(A) = speed of A

5 = [100 ÷ {s(A) - 150}]
5 × [s(A) - 150] = 100
5s(A) - 750 = 100
5s(A) = 100 + 750 = 850
s(A) = 850 ÷ 5 = 170 m/min

time taken for A to catch up C = 10 mins
time taken for A to catch up C = [400 ÷ {170 - s(C)}] , where s(C) = speed of C

10 = [400 ÷ {170 - s(C)}]
10 × [170 - s(C)] = 400
1700 - 10s(C) = 400
10s(C) = 1700 - 400 = 1300
s(C) = 1300 ÷ 10 = 130 m/min

time taken for B to catch up C = 300 ÷ (150 - 130)
=300 ÷ 20 = 15 mins

0900 + 15 mins = 0915

Bernard (B ) overtook Chi Hao (C) at 9.15 am.

==========

Q2.

Vol (1/6 filled) = (40 × 30 × 40) ÷ 6 = 8000 cm3
Inflow of water from tap X (2 mins) = 2 × 3 = 6 litres = 6000 cm3

At 0932, Vol of water in tank = 8000 + 6000 = 14000 cm3

14000 ÷ (40 × 30 × 40) = (7/24) filled (at 0932)

At 0943, tank was 75% filled = 0.75 × (40 × 30 × 40) = 36000 cm3

This is also equivalent to (3/4) = (18/24) filled

From 0932 - 0943 (with both taps X, Y turned on),
(18/24) - (7/24) = (11/24) filled in 11 mins

To fill up to the brim, another (1/4) or (6/24) needs to be filled.

Time taken to fill (6/24):
11 × (24/11) × (6/24) = 6 mins

Time (when filled to the brim):
0943 + 6 min = 0949

=========

Trust this helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: achieve_goal (offline)  Wednesday, June 26 2013 @ 02:57 AM CDT
achieve_goal

Hi, thank you for the maths solution.

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Wednesday, June 26 2013 @ 08:51 PM CDT
echeewh

Hey there,

Worked solution for Q1 was posted on 27 Jun.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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