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By: grace0306 (offline)  Friday, June 15 2012 @ 07:30 PM CDT (Read 1244 times)  
grace0306

Please help me with the following question..

Darren was driving along a road at a constant speed of 75km/h. He saw a motorcycle 750m behind him. The motorcycle was moving at 100km/h and drove past Darren's car after Darren had driven another 2.25km. 8 minutes after the speeding motorcycle had overtaken him, Darren passed the motorcycle. The motorcycle had beev stopped by a traffic police office. If both vehicles were moving at the constant speed,

(a) how long did it take the motorcycle to drive past Darren's car after Darren first spotted it?

(b) how many minutes had the speeding motorcycle been stopped before Darren drove past it?

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By: GIM (offline)  Sunday, June 17 2012 @ 05:11 AM CDT  
GIM

(-------0.75Km-------)(------------2.25Km---------)(-------------------8minutes---------------------)
M-----------------------D------------------------------(M)overtook(D)---------------------------------(D)overtook(M)

M speed =100Km/h
D speed = 75Km/h

a) M distance travelled = 0.75 + 2.25 = 3 Km
Time taken = 100/3 = 33.33h

b) D dist travelled in 8 minutes = (75Km/h) / (8/60h) = 562.5 Km
Time taken by M to travelled the same distance = (100km/h) / 562.5Km = 8/45 h= 10.67minutes
Length of Time M stopped = 10.67 - 8 = 2.67 minutes

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By: echeewh (offline)  Monday, June 18 2012 @ 08:17 PM CDT  
echeewh

hi Grace,

Pls refer to mistakes made by GIM in his worked solution for both (a) and (b) as shown:

(a)
Time taken = 100/3 = 33.33h

Time = Distance / Speed

(b)
D dist travelled in 8 minutes = (75Km/h) / (8/60h) = 562.5 Km

Distance = Speed x Time

+++++++++++++++++++++++++

Kindly refer to Correction as follows:

(***) = to buffer up for alignment purpose.


*****S(D)=75km/h**D1**************D2
******|->*************|->***************|->
|------|------------------|--------------------|----------------|
M****D
<----><---------------><------------------>
750m****2.25km*********8 mins
|->******************|->***************|->
S(M)=100km/h****M1**************M2

(a)
D(M) = 2.25km + 0.75km = 3km
Time taken by M to pass D = D(M) ÷ S(M) = 3 ÷ 100 = 0.03 hr = 1.8 min

(b)
D(D1) (covered in 8 mins) = 75 x (8/60) = 10 km
T(M1) (to travel 10 km) = 10 ÷ 100 = 0.1 hr = 6 mins
Hence, M had been stopped for 2 mins ( 8 - 6 = 2 mins).

=========================================

Trust this helps.

Do let me know if this does not agree with your answerkey.

Cheers,
Edward

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By: GIM (offline)  Saturday, June 23 2012 @ 04:19 AM CDT  
GIM

Oops! sorry for the mistake.

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