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# In a kilometre race, A gives B a start of 50 metres and

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Senior Manager
Joined: 30 Aug 2003
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In a kilometre race, A gives B a start of 50 metres and [#permalink]

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13 Mar 2004, 16:24
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In a kilometre race, A gives B a start of 50 metres and still beats him by 50 metres. On the other hand, if A gives B a start of 20 seconds, he beats him by 5 seconds. How long does A take to run the course?

250 seconds
200
180
225
None of the above
_________________

Pls include reasoning along with all answer posts.
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Kudos [?]: 25 [0], given: 0

Manager
Joined: 16 Jan 2004
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Location: NJ

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14 Mar 2004, 11:55
I get 250.

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Manager
Joined: 10 Mar 2004
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14 Mar 2004, 12:09
I will go for d i.e 225.

1. Let the speed of A be 'a' m/s.
2. B covers 900 m when A covers 1000 m.(from 1st statement of ques.)
3. From 1 and 2. Speed of B = (9a/10) m/s.
4. Time taken by B = (1000)/(9a/10) = 10000/9a seconds(using 3)
5. Time taken by A = (time taken by B - 25) seconds (using statement 2 of question)

= ((10000/9a) - 25) seconds
6. Time taken by A is also equal to 1000/a seconds
7. Equating 6 and 7, we get

Speed of A = a= 40/9 m/s

8. Thus time taken by a = (1000)/(40/9) = 25*9 = 225 seconds.

cheers

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14 Mar 2004, 12:09
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