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 By: Kuro (offline)  Sunday, August 24 2014 @ 03:03 AM CDT (Read 1542 times)
Kuro

Q1. Refer to attachment.

Q2. Charen, Ella and Sharon took part in a 200-metre race. All the girls were travelling at a constant speed throughout the race and each girl's speed was different. When Charen completed the race, Ella and Sharon were 40m and 60m away from the finishing line respectively. How far was Sharon from the finishing line when Ella finished the race?

Junior

Registered: 12/31/06
Posts: 27

 By: echeewh (offline)  Monday, August 25 2014 @ 02:50 AM CDT
echeewh

Hey <Kuro>

Following is my worked solution for Q2.

<---------------------- 200 --------------------------->
|---------------------------------------------------------|
|-> ********************************************* |->
C ********************************************** C1
s(C)
************************************* <--- 40 --->
|-> ********************************* |-> ******* |->
E ********************************** E1 ******* E2
s(E)
********************************** <----- 60 ----->
|-> ****************************** |-> ***** |->
S ******************************* S1 ***** S2
s(S)

By the time C completed race,
t(CC1) = t(EE1) = t(SS1)

t(CC1) = [200/s(C)]
t(EE1) = [160/s(E)]
t(SS1) = [140/s(S)]

So ...
[160/s(E)] = [140/s(S)]
[s(E)/S(S)] = (160/140) = (8/7)

s(E) : s(S)
8 : 7

By the time E completed race,
t(E1E2) = t(S1S2)

Since time taken is constant / common,
Distance ratio = Speed ratio

Given that the girls ran at constant speed throughout race,

s(E) : s(S)
8 : 7
d(E1E2) : d(S1S2)
8 : 7

8u --> 40
1u --> 5

d(S1S2) = 7u --> 7 × 5 = 35 m

60 - 35 = 25 m

========

Active Member

Registered: 04/21/11
Posts: 627

 By: echeewh (offline)  Tuesday, August 26 2014 @ 03:15 AM CDT
echeewh

hey <Kuro>

Kindly refer to attachment for worked solution to Q1.

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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