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Friday, November 17 2017 @ 10:20 PM CST
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By: Tping (offline)  Saturday, August 31 2013 @ 10:59 AM CDT (Read 601 times)  
Tping

Hi please help..

Q1
Town X and Y were 600km apart.
A lorry started travelling at a constant speed from Town X towards Town Y at 2.40p.m.
A car started travelling at a constant speed from Town X towards Town Y 1 ½ hours later.
The car overtake the lorry at 10.10p.m. when both were 60km from Town Y.
a) What was the speed of the car?
b) How much earlier did the car reach Town Y than the lorry?

Thank you.

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By: echeewh (offline)  Saturday, August 31 2013 @ 07:39 PM CDT  
echeewh

hey <Tping>

It is much appreciated if you can provide the <Answerkey> in advance, whenever possible. Thank you.


Following is my worked solution:

*** - for alignment purpose


X ******************************* Y
|------------------------------------------|
|-> ********* |-> ************ |->
L ********** L1 ************ L2
t1=1440 *** t2=1610 ***** t3=2210

|-> ************************* |->
C ************************** C1
t2=1610 ******************* t3=2210


1440 + 1 30 = 1610

d(L2Y) = 60 km = d(C1Y)
d(XY) = 600 km
so d(CC1) = 600 - 60 - 540 km

(a)
s(C) = d(CC1) ÷ t(CC1)
= 540 ÷ 6 = 90 km/h

(b)
s(L) = 540 ÷ 7.5 = 72 km/h
t(L2Y) = 60 ÷ 72 = (5/6) h

t(C1Y) = 60 ÷ 90 = (2/3) h

time earlier (of C) = (6/5) - (2/3) = (8/15) hr = 32 mins

Hence, the car reached Y 32 minutes earlier.

========

Trust this helps

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

Cheers,
Edward

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